Electrochemistry at the Nanoscale

Nanostructure Science and Technology

For other titles published in this series go to, http://www.springer.com/series/6331

Patrik Schmuki · Sannakaisa Virtanen Editors

Electrochemistry at the Nanoscale

123

Editors Patrik Schmuki University of Erlangen-Nuernberg Erlangen, Germany [email protected]

ISSN 1571-5744 ISBN 978-0-387-73581-8 DOI 10.1007/978-0-387-73582-5

Sannakaisa Virtanen University of Erlangen-N¨urnberg Erlangen, Germany [email protected]

e-ISBN 978-0-387-73582-5

Library of Congress Control Number: 2008942146 c Springer Science+Business Media, LLC 2009  All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com

Preface

For centuries, electrochemistry has played a key role in technologically important areas such as electroplating or corrosion. Electrochemical methods are receiving increasing attention in rapidly growing fields of science and technology, such as nanosciences (nanoelectrochemistry) and life sciences (organic and biological electrochemistry). Characterization, modification, and understanding of various electrochemical interfaces or electrochemical processes at the nanoscale have led to a huge increase of scientific interest in electrochemical mechanisms as well as in application of electrochemical methods to novel technologies. Electrochemical methods carried out at the nanoscale lead to exciting new science and technology; these approaches are described in 12 chapters. From the fundamental point of view, nanoscale characterization or theoretical approaches can lead to an understanding of electrochemical interfaces at the molecular level. Not only is this insight of high scientific interest, but also it can be a prerequisite for controlled technological applications of electrochemistry. Therefore, the book includes fundamental aspects of nanoelectrochemistry. Then, most important techniques available for electrochemistry on the nanoscale are presented; this involves both characterization and modification of electrochemical interfaces. Approaches considered include scanning probe techniques, lithography-based approaches, focused-ion and electron beams, and procedures based on self-assembly. In classical fields of electrochemistry, such as corrosion, characterizing surfaces with a high lateral resolution can lead to an in-depth mechanistic understanding of the stability and degradation of materials. The nanoscale description of corrosion processes is especially important in understanding the initiation steps of local dissolution phenomena or in detecting dissolution of highly corrosion-resistant materials. The latter can be of crucial importance in applications, where even the smallest amount of dissolution can lead to a failure of the system (e.g., release of toxic elements and corrosion of microelectronics). Since many electrochemical processes involve room-temperature treatments in aqueous electrolytes, electrochemical approaches can become extremely important whenever living (bio-organic) matter is involved. Hence, a strong demand for electrochemical expertise is emerging from biology, where charged interfaces play an important role. Interfacial electrochemistry is crucially important for understanding v

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Preface

the interaction of inorganic substrates with the organic material of biosystems. Thus, recent developments in the field of bioelectrochemistry are described, with a focus on nanoscale phenomena in this field. Electrochemical methods are of paramount importance for fabrication of nanomaterials or nanostructured surfaces. Therefore, several chapters are dedicated to the electrochemical creation of nanostructured surfaces or nanomaterials. This includes recent developments in the fields of semiconductor porosification, deposition into templates, electrodeposition of multilayers and superlattices, as well as self-organized growth of transition metal oxide nanotubes. In all these cases, the nanodimension of the electrochemically prepared materials can lead to novel properties, and hence to novel applications of conventional materials. We hope that this book will be helpful for all readers interested in electrochemistry and its applications in various fields of science and technology. Our aim is to present to the reader a comprehensive and contemporary description of electrochemical nanotechnology.

Contents

Theories and Simulations for Electrochemical Nanostructures . . . . . . . . . . . E.P.M. Leiva and Wolfgang Schmickler

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SPM Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 O.M. Magnussen X-ray Lithography Techniques, LIGA-Based Microsystem Manufacturing: The Electrochemistry of Through-Mold Deposition and Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 James J. Kelly and S.H. Goods Direct Writing Techniques: Electron Beam and Focused Ion Beam . . . . . . . 139 T. Djenizian and C. Lehrer Wet Chemical Approaches for Chemical Functionalization of Semiconductor Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Rabah Boukherroub and Sabine Szunerits The Electrochemistry of Porous Semiconductors . . . . . . . . . . . . . . . . . . . . . . . 249 John J. Kelly and A.F. van Driel Deposition into Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Charles R. Sides and Charles R. Martin Electroless Fabrication of Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 T. Osaka Electrochemical Fabrication of Nanostructured, Compositionally Modulated Metal Multilayers (CMMMs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 S. Roy Corrosion at the Nanoscale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Vincent Maurice and Philippe Marcus vii

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Nanobioelectrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 A.M. Oliveira Brett Self-Organized Oxide Nanotube Layers on Titanium and Other Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 P. Schmuki Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

Contributors

Rabah Boukherroub Biointerfaces Group, Interdisciplinary Research Institute (IRI), FRE 2963, IRI-IEMN, Avenue Poincar´e-BP 60069, 59652 Villeneuve d’Ascq, France, [email protected] Thierry Djenizian Laboratoire MADIREL (UMR 6121), Universit´e de Provence-CNRS, Centre Saint J´erˆome, F-13397 Marseille Cedex 20, France, [email protected] A. Floris van Driel Condensed Matter and Interfaces, Debye Institute, Utrecht University, P.O. Box 80000, 3508 TA, Utrecht, The Netherlands, [email protected] Steven H. Goods Dept. 8758/MS 9402, Sandia National Laboratories, Livermore, CA 94550, USA, [email protected] James J. Kelly IBM, Electrochemical Processes, 255 Fuller Rd., Albany, NY 12203, USA, [email protected] John J. Kelly Condensed Matter and Interfaces, Debye Institute, Utrecht University, P.O. Box 80000, 3508 TA, Utrecht, The Netherlands, [email protected] Christoph Lehrer Lehrstuhl f¨ur Elektronische Bauelemente, Universit¨at ErlangenN¨urnberg, Cauerstr. 6, 91058 Erlangen, Germany, [email protected] Ezequiel P.M. Leiwa Universidad Nacional de Cordoba, Unidad de Matematica y Fisica, Facultad de Ciencias Quimicas, INFIQC, 5000 Cordoba, Argentina, [email protected] Olaf M. Magnussen Institut f¨ur Experimentelle und Angewandte Physik, Christian-Albrechts-Universit¨at zu Kiel, 24098 Kiel, Germany, [email protected] Philippe Marcus Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR 7045) Ecole Nationale Sup´erieure de Chimie de Paris, Universit´e Pierre et Marie Curie, 11, rue Pierre et Marie Curie, 75005 Paris, France, [email protected] ix

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Contributors

Charles R. Martin Department of Chemistry, University of Florida, PO Box 117200, Gainesville, FL 32611, USA, [email protected] Vincent Maurice Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR 7045), Ecole Nationale Sup´erieure de Chimie de Paris, Universit´e Pierre et Marie Curie, 11, rue Pierre et Marie Curie, 75231 Paris Cedex 05, France, [email protected] Ana Maria Oliveira Brett Departamento de Quimica, Universidade de Coimbra, 3004-535 Coimbra, Portugal, [email protected] Tetsuya Osaka Department of Applied Chemistry, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan, [email protected] Sudipta Roy School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK, [email protected] Wolfgang Schmickler Department of Theoretical Chemistry, University of Ulm, D-89069 Ulm, Germany, [email protected] Patrik Schmuki University of Erlangen-Nuremberg, Department for Materials Science, LKO, Martensstrasse 7, D-91058 Erlangen, Germany, [email protected] Charles R. Sides Gamry Instruments, Inc., 734 Louis Drive, Warminster, PA 18974-2829, USA, [email protected] Sabine Szunerits INPG, LEMI-ENSEEG, 1130, rue de la piscine, 38402 Saint Martin d’Her`es, France, [email protected]

Theories and Simulations for Electrochemical Nanostructures E.P.M. Leiva and Wolfgang Schmickler

1 Introduction Electrochemical nanostructures are special because they can be charged or, equivalently, be controlled by the electrode potential. In cases where an auxiliary electrode, such as the tip of a scanning tunneling microscope, is employed, there are even two potential drops that can be controlled individually: the bias potential between the two electrodes and the potential of one electrode with respect to the reference electrode. Thus, electrochemistry offers more possibilities for the generation or modification of nanostructures than systems in air or in vacuum do. However, this advantage carries a price: electrochemical interfaces are more complex, because they include the solvent and ions. This poses a great problem for the modeling of these interfaces, since it is generally impossible to treat all particles at an equal level. For example, simulations for the generation of metal clusters typically neglect the solvent, while theories for electron transfer through nanostructures treat the solvent in a highly abstract way as a phonon bath. Therefore, a theorist investigating a particular system must decide, in advance, which parts of the system to treat explicitly and which parts to neglect. Of course, to some extent this is true for all theoretical research, but the more complex the investigated system, the more difficult, and debatable, this choice becomes. There is a wide range of nanostructures in electrochemistry, including metal clusters, wires, and functionalized layers. Not all of them have been considered by theorists, and those that have been considered have been treated by various methods. Generally, the generation of nanostructures is too complicated for proper theory, so this has been the domain of computer simulations. In contrast, electron transfer through nanostructures is amenable to theories based on the Marcus [1] and Hush [2] type of model. There is little overlap between the simulations and the theories, so we cover them in separate sections. W. Schmickler (B) Department of Theoretical Chemistry, University of Ulm, D-89069 Ulm, Germany e-mail: [email protected]

P. Schmuki, S. Virtanen (eds.), Electrochemistry at the Nanoscale, Nanostructure Science and Technology, DOI 10.1007/978-0-387-73582-5 1,  C Springer Science+Business Media, LLC 2009

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E.P.M. Leiva and W. Schmickler

Nanostructures in general are a highly popular area of research, and there is a wealth of literature on this topic. Of course, electrochemical nanostructures share many properties with nonelectrochemical structures; in this review we will focus on those aspects that are special to electrochemical interfaces, and that therefore depend on the control of potential or charge density. We shall start by considering simulations of electrochemical nanostructures, and shall then turn toward electron transfer through such structures, in particular through functionalized adsorbates and films.

2 Simulations of Electrochemical Nanostructures As mentioned in the introduction, electrochemistry offers an ample variety of possibilities for the generation of nanostructures, some of which are illustrated in Fig. 1. In this figure, we concentrate on the type of nanostructures that can be obtained by the application of a scanning probe microscope (SPM), which is the general denomination of a device used to image materials at the nanometer scale. In the case of surface imaging, the sensitivity of the SPM device to some property of the surface (local electronic density of states, chemical nature, electronic dispersive forces) is used to get some topological information. However, our current interest is related to the possibility of using the SPM arrangement to change the atomic ordering and eventually the chemical nature of the surface. Figure 1a shows the so-called tip-induced local metal deposition, where a scanning tunneling microscope (STM) tip is first loaded via electrochemical deposition with a foreign metal; then the tip is moved to the surface of a substrate, and, upon retraction, a cluster is left behind on the surface. This method works for a number of adsorbate/substrate combinations, but for others it does not, and computer

Fig. 1 Schematic illustration of several electrochemical techniques employed for surface nanostructuring: (a) Tip-induced local metal deposition; (b) defect nanostructuring; (c) localized electrochemical nucleation and growth; (d) electronic contact nanostructuring; and (e) scanning electrochemical microscope

Theories and Simulations for Electrochemical Nanostructures

3

simulations have contributed to understanding the formation of the clusters. Figure 1b illustrates a different procedure, where a hole is generated by applying a potential pulse to the STM tip. Then the potential of the substrate is changed to allow controlled metal electrodeposition into the cavity. Computer simulations of this type of processes are in a developing stage, with promising results. The method depicted in Fig. 1c also starts with metal deposition on the tip, but the metal is then dissolved by a positive potential pulse that produces local oversaturation of the metal ions, which subsequently nucleate on the surface. Some aspects of this problem have been discussed by solving the diffusion equations for the ions generated at the tip. Combinations of techniques (b) and (c) exist, where a foreign metal is deposited on the tip, and a double pulse is applied to it. The first pulse generates a defect on the surface, and the second pulse desorbs adatoms from the tip that nucleate into the defect. This method has been simulated using Brownian dynamics. The method depicted in Fig. 1d) is employed to generate defects on the surface by means of some type of electronic contact between the tip and the surface and has not been modeled so far. Finally, the method depicted in Fig. 1e involves the generation of some species on the tip that further may react with the surface. This is the basis of the technique denominated scanning electrochemical microscopy. While it can be used to image regions of the surface with different electrochemical properties, it can also be applied to modify, at will, the surface if the latter reacts with the species generated at the tip. Due to technical limitations, this technique has generally been applied in the micrometric rather than in the nanometric scale, but it is a matter of improvement to shift its application into the nanometer range.

2.1 Computer Simulation Techniques for Nanostructures The term computer simulation is so widely used that here a short comment is required to clarify the matter. The term simulation is often applied to various numerical methods for studying the time dependence of processes. In fact, computers may be used to solve numerically numerous problems that range from phenomenological equations to sophisticated quantum mechanical calculations. An electrochemical example for the former is the simulation of voltammetric profiles by solving the appropriate diffusion equations coupled to an electron-transfer reaction. On the other end of the simulation methods, the time-dependent Schr¨odinger equation may be solved to study dynamic processes in an ensemble of particles. Here we refer only to simulations on an atomic scale. In the simulations of electrochemical nanostructures, we have to deal with a few hundreds or even thousands of atoms; purely quantum-mechanical calculations of the ab initio type are still prohibitive for current computational capabilities. However, since it is expected that at the nanometric scale the atomic nature of atoms may play a role, it is desirable that the methodology should reflect atomic nature of matter, at least in a simplified way. We shall return to this point below. A typical atomistic computer simulation consists in the generation of a number of configurations of the system of interest, from which the properties in which we are

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interested are calculated. From the viewpoint of the way in which the configurations are generated, the simulations methods are classified into deterministic or stochastic. In the first case, a set of coupled Newton’s equations of the type: mi

d2 ri = f i (t) dt 2

(1)

is solved numerically, where the atomic masses m i and the positions ri are related to the forces f i (t) experimented by the particle i at the time t. These forces are calculated from the potential energy of the system U (rn ): fi = −∇U (rn )

(2)

where we denote with rn the set of coordinates of the particles constituting the system. Since Eq. (1) contains the time, it is clear that this type of method allows obtaining dynamic properties of the system. A typical algorithm that performs the numerical task is, for example, the so-called velocity Verlet algorithm: ri (t + ⌬t) = ri (t) + vi (t)⌬t +

1 f i (t) 2 ⌬t 2 mi

(3)

where vi (t) is the velocity of the particle at time t and ⌬t is an integration step. The recurrent application of this equation to all the particles of the system leads to a trajectory in the phase space of the system, from which the desired information may be obtained. We can get a feeling for the ⌬t required for the numerical integration by inserting into Eq. (3) some typical atomic values. If we want to get a small atomic ˚ for a mass of the displacement ⌬ri = ri (t + ⌬t) − ri (t), say of the order of 10−3 A ˚ , we get: order of 10−23 g, subject to forces of the order of 10−1 eV/A  ⌬t = O

10−23 g × 10−11 cm eV 107 cm × 1.6 × 10−12 erg eV

 = O(10−15 s)

(4)

where 1.6 × 10−12 erg/eV is a conversion factor. The result obtained in Eq. 4 means that the integration time required is of the order of a femtosecond, so that a few million of integration steps will lead us into the nanosecond scale, which are the typical simulation times we can reach with current computational resources in nanosystems. The simulation method discussed so far is the so-called atom or molecular dynamics (MD) procedure and can be employed to calculate both equilibrium and nonequilibrium properties of a system. In molecular dynamics the generated configurations of the system follow a deterministic sequence. However, the trajectory of the system in configuration space may be chosen differently, following some rules that allow one to obtain sets of coordinates of the particles that may later be employed to calculate equilibrium properties. Thus, the main idea underlying stochastic simulation methods is, as in MD, to generate a sequence of configurations. However, the transition probabilities between

Theories and Simulations for Electrochemical Nanostructures

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them are chosen in such a way that the probability of finding a given configuration is given by the equilibrium probability density of the corresponding statistical thermodynamic ensemble. Making a short summary of equilibrium statistical thermodynamics, we recall that the first postulate states that an average over a temporal behavior of given a physical system can be replaced by the average over a collection of systems or ensemble that exhibits the same thermodynamic but different dynamic properties. The second postulate refers to isolated systems, where the volume V , the energy E, and the number of particles N are fixed, and states that the systems in the ensemble are uniformly distributed over all the quantum states compatible with the N V E conditions. Besides the N V E or microcanonical ensemble, some other popular ensembles are the canonical ensemble (constant number of particles, volume, and temperature), denoted as N V T , the isothermal isobaric ensemble or N PT ; and the grand canonical ensemble, where the variables fixed are the chemical potential, volume, and the temperature (μV T ensemble). The molecular dynamics procedure described above is usually run in the (N V E) or NVT ensemble, but other conditions are also possible. Returning to the stochastic simulation methods, and taking the NVT ensemble as an example, the transitions between the different configurations are chosen in such a way that the equilibrium probability density of a certain configuration rn will be given by: exp (−U (rn )/kT ) ρ(rn ) =  exp (U (r)/kT ) dr where the integral in the denominator runs over all the possible configurations of the system. A way to generate such probability transitions between configurations is that proposed by Metropolis:  mn

= αmn

ρ(rn ) = αmn exp [(U (rm ) − U (rn )) /kT ] if ρ(rn ) < ρ(rn ) ρ(rm )  = αmn if ρ(rn ) < ρ(rn )

(5)

mn

where ⌸mn is the transition probability from state m to state n, and αmn are constants which are restricted to be elements of a symmetric matrix. Thus, a given transition probability ⌸mn is obtained by calculating the energy of the system in state m, say U (rn ) and the energy in the state n, say U (rm ). The configuration in the n state, given by the vector rn , is obtained from rm by allowing some random motion of the system. For example, a particle i may be selected at random, and its coordinates are displaced from their position rni with equal probability to any point rmi inside a small cube surrounding the particle. To accept the move with a probability of exp [− (U (rn ) − U (rm )) /kT ] , a random number ξ is generated with uniform probability density between 0 and 1. If ξ is lower than exp [− (U (rn ) − U (rm )) /kT ] it is accepted, otherwise it is rejected. Alternatively, the simultaneous move of all the particles may be attempted. Similarly to the procedure described above, the energy

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values before and after the move attempt to determine the transition probability. The intensive use this technique makes of random (or better stated pseudo-random) numbers has earned it the name of Monte Carlo(MC) method. In the case of grand canonical or μV T simulations, in addition to the motion of the particles, attempts are taken to insert into or remove particles from the system. In this case, all simulation moves must be done in such a way that the probability density of obtaining a given configuration rn of a system of N particles is given by: exp [− (U (rn ) + Nμ) /kT ] ρ(rn , N) =   exp [− (U (r) + Nμ) /kT ] dr N Grand canonical simulations are very useful for simulating electrochemical systems, because a constant electrode potential is equivalent to a constant chemical (or electrochemical) potential.

2.2 Interaction Potentials The main difficulty of computer simulations is that a knowledge of the function potential energy functions U (rn ) is required to calculate the forces in atom dynamics or to calculate the transition probabilities in MC. Strictly speaking, U (rn ) stems from the quantum-mechanical interactions between the particles of the system, so that it should be obtained from first-principles calculations. However, for large ensembles this is not possible, so approximations, or model potentials, are needed. Such potentials are available for many systems: for example, for ionic oxides, closed-shell molecular systems, and fortunately for the problem at hand, for transition metals and their alloys. To the latter class of models belong the so-called glue model or the embedded atom method (EAM) [3]. Within the pair-functional scheme, the EAM proposes that the total energy U (rn ) of any arrangement of N metal particles may be calculated as the sum of individual particle energies E i U (rn ) =

N 

Ui

i=1

where the Ui are Ui = Fi (ρh,i ) +

1 Vi j (ri j ) 2 j =i

(6)

Fi is the embedding function and represents the energy necessary to embed atom i into the electronic density ρh,i . This latter quantity is calculated at the position of atom i as the superposition of the individual atomic electronic densities ρi (ri j ) of the other particles in the arrangement as:

Theories and Simulations for Electrochemical Nanostructures

ρh,i =



7

ρi (ri j )

j =i

The attractive contribution to the energy is given by the embedding function Fi , which contains the many-body effects in EAM. The repulsive interaction between ion cores is represented as a pair potential, Vi j (ri j ) which depends exclusively on the distance between each pair of interacting atoms and has the form of a pseudocoulombic repulsive energy: Vi j =

Z i (ri j )Z j (ri j ) ri j

where Z i (ri j ) may be considered as an effective charge, which depends upon the nature of particle i . This potential has been adequately parametrized from experimental data so as to reproduce a number of parameters as equilibrium lattice constants, sublimation energy, bulk modulus, elastic constants and vacancy formation energy.

2.3 The Creation of Atomic Clusters with the Aid of an STM Tip As shown in Fig. 1a, an efficient electrochemical method to generate metal clusters on a foreign metal surface consist in moving a metal-loaded tip toward a surface of different nature. The onset of the interaction between the tip and the surface produces an elongation of the tip at the atomic scale – the so-called jump to contact – that generates a connecting neck between the tip and the surface. After this, the tip may approach further, and can be retracted at different penetration stages, with various consequences for the generated nanostructure. Experiments with several systems show that this procedure works with several tip/sample combinations, but with others it fails to produce well-defined surface features. For example, a model system for this type of procedure is Cu, deposited on the STM tip, and squashed against a Au(111) surface; for this combination of metals, an array of 10,000 clusters may be produced in a few minutes [4]. Similarly, with the system Pd/Au(111) well-defined nanostructures have been generated [5]. On the other hand, attempts to generate Cu clusters on Ag(111) failed; only dispersed monoatomic-high islands have been observed [6]. The systems Ag/Au(111) and Pb/Au(111) exhibit of an intermediate behavior, presenting a wide scatter of cluster sizes and poor reproducibility [6]. Since the creation of the clusters is a dynamic process, the natural computational tool to study this process appears to be molecular (or more properly stated) atom dynamics. In this respect, it is worth mentioning the pioneering work of Landman et al. [7], who employed this method to investigate the various atomistic mechanisms that occur when a Ni tip interacts with a Au surface. This investigation established a number of features that were relevant to understand the operating mechanism: on the one hand, during the onset of the tip–surface interaction, the occurrence of a mechanical instability leading to the formation of the connecting neck between tip and surface mentioned above. On the other hand, and in the subsequent stages

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of the nanostructuring process, the existence of a sequence of elastic and plastic deformation phases that determine the final status of the system. Typically, due to the time-step limitations mentioned above, the simulations are restricted to a few nanoseconds. However, the electrochemical generation of nanostructures involves times of the order of milliseconds, so that some long-time features of the experimental problem will be missing in the simulations. This must be taken into account for a careful interpretation of the experimental results in terms of simulations, in the sense that some slow processes, not observed in the simulations, may occur in experiments. However, the information obtained in the computational studies is important in the sense that if some processes are observed, they will certainly occur in the experiments. A typical atomic arrangement employed for a MD simulation of the generation of clusters is shown in Fig. 2. The simulated tip consists of a rigid core, in the present case of Pt atoms, from which mobile atoms of type M to be deposited are suspended. These amount typically to a couple of thousand atoms, the exact figures for the different systems can be found in reference [8]. Different structures were assumed for the underlying rigid core. In some simulations a fcc crystalline structure was assumed, oriented with the (111), or alternatively the (100), lattice planes facing the substrate. We shall call them [111] and [100] tips, respectively.

Fig. 2 x − y section of a typical atomic arrangement employed in the simulation of tip-induced local metal deposition. Dark circles represent atoms belonging to the STM tip. Transparent circles denote the atoms of the material M being deposited, and light gray circles indicate the substrate atoms. The presence of a monolayer adsorbed on the electrode is depicted in this case. dts indicates the distance between the surface and the upper part of the tip. d0 is the initial distance between the surface and the lower part of the tip. Mobile and fixed substrate layers are also marked in the figure. Taken from reference [8].

Theories and Simulations for Electrochemical Nanostructures

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In other simulations, an amorphous structure was assumed [9]. The substrate S was represented by six mobile atom layers on top of two static layers with the fcc(111) orientation. An adsorbed monolayer of the same material as that deposited on the tip was occasionally introduced, so simulate nanostructuring under underpotential deposition conditions. Periodic boundary conditions were applied in the x − y plane, ˚ steps, parallel to the substrate surface. The tip was moved in z direction in 0.006 A performing first a forward motion toward the surface followed by a stage of backward motion. The distances given below will be referred to the jump-to-contact point described above, and the turning point of the motion of the tip, which determines the magnitude of the indentation, will be denoted with dca . The metallic systems so far investigated were Cu/Au(111), Pd/Au(111), Cu/Ag(111), Pb/Au(111), Ag/Au(111), and Cu/Cu(111). Figure 3 depicts several snapshots of a typical simulation run where cluster creation is successful, in this case for the system Pd[110]/Au(111). The simulation starts at a point where the tip–surface interaction is negligible (Fig. 3a). The

Fig. 3 Snapshots of an atom dynamics simulation taken during the generation of a Pd cluster on Au(111): (a) initial state; (b) jump-to-contact from the tip to the surface; (c) closest approach distance; (d) connecting neck elongation; and (e) final configuration. The resulting cluster has 256 atoms, is eight layers high and its composition is 16% in Au. Taken from reference [10]

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approach of the tip to the surface leads to the jump-to-contact process, where mechanical contact between the tip and the surface sets in (Fig. 3b). A further approach of the tip results in an indentation stage (Fig. 3c), where the interaction between the tip and the surface is strong enough to produce mixing between M and S atoms. Figure 3d and e present the stages preceding and following the breaking of the connecting neck, leaving a cluster on the surface. A systematic study using different dca allows a more quantitative assessment of the nature of the nanostructures generated. Figure 4 shows the cluster size and height as a function of the distance of closest approach. It is clear that a deeper indentation of the tip generates larger and higher clusters. However, this is accompanied by an enrichment of the cluster in Au content, which in the simulations reported here reaches up to 16%. Extensive simulations showed that the nature of the clusters formed depends on the fact whether or not the surface is covered by a monolayer of Pd. In the former case, rather pure Pd clusters are formed with the [110]-type tip. However, the structure of the tip also plays a role in the mixing between substrate and tip atoms. In fact, the protective effect of the adlayer disappears when a [111] Pd tip is employed, and alloyed clusters are obtained. Simulation studies performed with a tip and a substrate of the same nature allowed to study pure tip structure effects [9]. In the case of the Cu/Cu(111) homoatomic system adatom exchange is found to take place in the case of the [111] tip almost exclusively. On the other hand, when nanostructuring is achieved with [110] type tips, the easy gliding along (111) facets allows the transfer of matter to the surface without major perturbations on the substrate. Figure 5 shows snapshots of a simulation where cluster creation fails, in this case Cu[111]/Ag(111). As in the previous case, Fig. 5a shows the appearance of

Fig. 4 Cluster size and composition for Pd nanostructuring on Au(111), as a function of deepest tip penetration z for a typical set of runs: (a) number of particles in the cluster and (b) cluster height in layers. The numbers close to the circles denote the Au atomic percentage in the clusters. Taken from reference [11]

Theories and Simulations for Electrochemical Nanostructures

11

Fig. 5 Snapshots of an atom dynamics simulation taken during a failed attempt to generate a Cu cluster on Ag(111): (a) jump-to-contact from the surface to the tip. Note that the jump-to-contact goes in the opposite direction to that of Fig. 4; (b) closest approach distance; (c) retraction of the tip ˚ above the closest approach distance; and (d) final state after the rupture of the connecting to 4.8 A neck. Thirty-eight Ag atoms were removed from the surface. Taken from reference [10]

a mechanical instability that generates the tip–surface contact. However, it must be noted that in the present case the surface atoms of the substrate participate actively in the processes, being lifted from their equilibrium position. In the present simulation, although the motion of the tip is restricted to a gentle approach to the surface (dca = ˚ Fig. 5b), the interaction is strong enough to dig a hole on the surface. Other −3.6 A, simulations where dca is more negative lead to larger holes, and some Cu atoms are dispersed on the surface. On the other hand, when a Cu[110] tip is used for this system, pure small Cu clusters result, which are, however, unstable. Simulations for the Cu/Au(111) system also lead to successful nanostructuring of the surface, with results qualitatively similar to those of Pd/Au(111). On the other hand, the Ag/Au(111) system yields poorly defined nanostructures, and something similar happens with the Pb/Au(111) system, where only pure Pb, tiny, unstable clusters are obtained [8, 12].

12

E.P.M. Leiva and W. Schmickler

Besides the generation mechanism of the clusters, the question of their stability is highly relevant for technological applications. Experiments show that they are surprisingly resistant against anodic dissolution [6]. For example, a Cu cluster on Au(111) at a potential of 9–10 mV Versus Cu/Cu+2 was found to be stable for at least 1 h. This fact is rather surprising, since due to surface effects, clusters should be less stable than the bulk material. In fact, atoms at the surface of a cluster are less coordinated than those inside the nanostructure, so that the average binding energy of the atoms in the cluster should be smaller than that of bulk Cu. A meaningful concept of the theory of the electrochemical stability of monolayers is the so-called underpotential shift ⌬φup , which was originally defined by Gerischer and co-workers [13] as the potential difference between the desorption peak of a monolayer of a metal M adsorbed on a foreign substrate S and the current peak corresponding to the dissolution of the bulk metal M. A more general definition of ⌬φup can be stated in terms of the chemical potentials of the atoms adsorbed on a foreign substrate at a coverage degree ⌰, say μ M⌰ (S) , and the chemical potential of the same species in the bulk μ M according to: ⌬φupd (⌰) =

1 (μ M − μ M⌰ (S) ) ze0

(7)

Following the same line, the electrochemical stability of a given nanostructure may be analyzed through the chemical potential of its constituting atoms. Thus, since the stability of the cluster on the surface is given by the chemical potential of the atoms μ, a grand-canonical simulation with μ as control parameter appears as the proper tool to study cluster stability. Further parameters in the experimental electrochemical systems are the temperature T and the pressure P, so that the proper simulation tool appears to be a μPT simulation, where the ensemble partition function is given by: ⌼=



e−Ui /kT e− pV /kT e N μ/kT

(8)

N,V,E i

However, for the usual experimental conditions, where solid species are involved and p = 1 atm, the sum in (8) can be replaced by: ⌼=



e−Ui /kT e N μ/kT

(9)

N,V,E i

where we have set p = 0. This equation contains volume-dependent terms through Ui , since the energy of the nanostructure depends on its volume. However, as shown above in Eq. (5), MC simulations do not involve the sum (9), but rather the ratio of probability densities between two states, that in the present case will be given by: ρn = βmn exp [(Um (V ) − Un (V )) /kT ] exp [Nμ/kT ] ρm

Theories and Simulations for Electrochemical Nanostructures

13

where we have written Um (V ) − Un (V ) to emphasize the fact that the energy is a function of the volume of the nanostructure. Although the partition function involved is a different one, this equation is formally identical to that obtained for a grand-canonical (GC, μVbox T ) simulation, where particles are created in and removed from a simulation box with volume Vbox containing the nanostructure. Note that although the volume Vbox is held constant when calculating transition probabilities in the GC simulations, these allow for the the fluctuation of the volume V , with the concomitant changes in the energy Um . As we have seen above, depending on the penetration of the tip into the surface, different degrees of mixing between the material of the tip and that of the substrate may be obtained, which can affect the stability of the clusters. The behavior of pure and alloyed clusters could be in principle studied by comparing the behavior of the different clusters formed in the MD simulations. However, since the energy of the clusters (and thus their chemical potential) is a function not only of their composition but also of their geometry (i.e., surface-to-volume ratio), and the clusters formed under different conditions present different geometries, direct comparison appears somewhat complicated. A way to circumvent this problem consists in considering an alloyed cluster, and replacing the atoms coming to the substrate by atoms of the nanostructuring material. In this way, the geometry at the beginning of the simulation should be approximately the same, apart from a slight stress that may be relaxed at the early stages of the simulation. Figure 6 shows in snapshots of a GCMC simulation, the comparative behavior of pure Pd, and alloyed Pd/Au clusters upon dissolution. In the case of the pure Pd clusters, it can be seen that, as the simulation proceeds, dissolution takes place from all layers, while the cluster tries to keep its roughly pyramidal shape. Hexagonally shaped structures, constituted by seven atoms, are found to be particularly stable. In the case of alloyed clusters, they become enriched in Au atoms as the simulation proceeds; simultaneously, the dissolution process is slowed down. This can be seen more quantitatively in Fig. 7, where the dissolution of a pure Pd and of an alloyed Pd/Au cluster is studied at a constant chemical potential. It can be noticed that the cluster remains relatively stable at chemical potentials close to 3.80 eV. This value is higher than the cohesive energy of Pd, −3.91 eV, showing that, as expected, the cluster is less stable than the bulk material. At higher values of μ the cluster starts to grow, at lower values it dissolves. Concerning the chemical potentials that allow cluster growth, both the pure and the alloyed clusters behave similarly. However, marked differences occur for values of μ at which the clusters are dissolved. While the pure Pd clusters dissolve rapidly, the alloyed clusters become more stable as the simulation proceeds as a consequence of their enrichment in Au atoms. The results compiled from simulations for different systems are summarized in Table 1, together with experimental information. We can draw two main conclusions from experiments and simulations. On the one side, the best conditions for cluster generation exist in those systems where the cohesive energies of the metal being deposited and the substrate are similar. On the other side, in systems where the alloy heats of solution ⌬Hd for single substitutional impurities is negative, the mixing of the atoms will be favored on thermodynamic grounds, and thus cluster stability will be improved.

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E.P.M. Leiva and W. Schmickler

Fig. 6 Different stages of a dissolution of a pure (a) and alloyed (b) Pd cluster on a Au(111) surface. The alloyed cluster was 16% in content of Au atoms and contained an initial number of 252 atoms

2.4 The Filling of Nanoholes In the previous section, we have seen how grand-canonical Monte Carlo simulations can be employed to understand experimental results for the localized metal deposition on surfaces. The same tool can be employed to consider the filling of surface defects like nanocavities, as explained above in Fig. 1b. Schuster et al. [20] have shown that the application of short voltage pulses to a scanning tunneling

15

n

n

Theories and Simulations for Electrochemical Nanostructures

Fig. 7 Evolution of cluster size (expressed in terms of number of atoms) as a function of the number of Monte Carlo steps at different chemical potentials. (a) Pure Pd cluster initially containing 252 atoms. (b) Alloyed Pd/Au cluster, initially containing 211 Pd and 41 Au atoms. Taken from reference [8] Table 1.1 Compilation of experimental and simulated systems according to their difference binding energy ⌬E coh and alloy heats of solution ⌬Hd for single substitutional impurities. Experimental results were taken from ref. [4, 14, 15, 16, 6, 17], the information corresponding to Ni–Au(111) simulations was taken from [7, 18]. ⌬E coh and ⌬Hd were taken from [19]. 3D-stable means that the clusters generated in the experiments endure dissolution. 3D-unstable means that experimental clusters dissolve easily. 2D means that only 2D islands were obtained. Hole refers to the fact that only holes were generated on the surface after the approach of the tip. Concerning the column of simulation, alloying means that the cluster contained not only atoms of the metal being deposited but also some coming from the substrate. Taken from reference [8] System

Experiment

Simulation

⌬E coh /eV

⌬Hd /eV

Pd/Au(111) Cu/Au(111) Ag/Au(111) Pb/Au(111) Cu/Ag(111) Ni/Au(111)

3D-Stable 3D-Stable 3D-Stable 3D-Unstable 2D hole

3D-alloying 3D-alloying 3D-alloying 3D-pure hole, 3D small hole

−0.02 −0.38 −1.08 −1.84 0.69 0.52

−0.36, −0.20 −0.13, −0.19 −0.16, −0.19 0.03, 0.01 +0.25, +0.39 +0.22, +0.28

microscopic tip close to a Au(111) surface may be employed to generate nanometersized holes. While the depth of the nanoholes only amounts 1–3 monolayers, their lateral extension is about 5 nm. The subsequent controlled variation of the potential applied to the surface immersed in a Cu+2 -containing solution leads to a progressive filling of the nanoholes in a stepwise fashion. This is illustrated in Fig. 8, where the time evolution of the height of the nanostructure (hole + cluster inside it) is given. It

16

E.P.M. Leiva and W. Schmickler

Fig. 8 Time evolution of the height of the nanostructure obtained by polarization at different potentials of a Au(111) surface with nanometer-sized holes. The nanostructure considered consists of a ca. 8-nm-wide hole in which Cu atoms are deposited by potential control. The potentials are referred to the reversible Cu/Cu+2 electrode in the same solution. Taken from reference [22]

is clear that the equilibrium height depends on the applied overpotential, indicating that the surface energy of the growing cluster is balanced by the electrochemical energy. The idea put forward by the authors was that the overpotential was related to the Gibbs energy change associated with the cluster growth. From this hypothesis, the authors estimated that boundary energy amounts 0.5 eV/atom for the present system. More recently, Solomun and Kautek [21] have studied the decoration of nanoholes on Au(111) by Bi and Ag atoms. While the Au nanoholes were completely filled by Bi at underpotentials, the Ag nanoholes remained unfilled, even at low overpotentials. In the latter case, only at the equilibrium potential and at overpotentials did the nanoholes start to be filled flat to the surface, showing no protrusion over it. As stated in the section on interaction potentials, a simulation containing all the electrochemical ingredients should involve in principle interfacial charging effects, solvent, and importantly the contribution of the long-ranged interaction of adsorbed anions, which in some systems such as Cu/Au play a key role in the stabilization of the underpotential deposits. However, simulations with the EAM potentials, which properly take into account interactions between metallic atoms, will give at least a qualitative idea of the leading contribution to the defect nanostructuring process. Figure 9 shows results of such a simulation, where the chemical potential was stepped to simulate the negative polarization of the surface, together with snapshots of the simulation. It can be seen that at chemical potentials μ close to the binding energy of bulk Cu (−3.61 eV), the Au nanohole, initially decorated by Cu atoms, suddenly fills up to a level close to substrate surface. Then, a further step in the height is found, and later the growth proceeds with the cluster aquiring a pyramid-like shape, slowly expanding beyond the borders of the nanohole. The calculation of boundary energy

Theories and Simulations for Electrochemical Nanostructures

17

Fig. 9 Growth of a Cu cluster inside a defect on a Au(111) surface. The number of Cu atoms is given as a function of the chemical potential of the Cu atoms μ. The snapshots were taken at the points marked by the arrows. Taken from reference [10]

using EAM yields values of the order of 0.1 eV atom, considerably lower than the experimental estimation. This low value is partially due to the inaccuracy of the potentials employed for the simulations – the higher experimental values are reasonable. If the experimental values were as low as the calculated ones, the stepwise growth of the nanostructure would not be observed clearly. In fact, the stepwise growth is a consequence of the fact that the border atoms make a sizable contribution to the free energy of the growing cluster, and this relative contribution becomes smaller as cluster size increases. In the limit of infinitely large clusters, no steps in the growth of the cluster would be observed. Furthermore, the experimental system presents a Cu layer deposited at underpotentials. The simulation do not show this layer, since no upd is predicted for this system. Rather than to an excess of the binding energy of the Cu/Au(111) system with respect to bulk Cu, the existence of the Cu upd overlayer has been attributed to anion effects [23].

3 Electron Transfer Through Functionalized Adsorbates and Films 3.1 Electron Exchange with a Monolayer Monolayers that self-assemble on electrode surfaces (SAMs) are a fascinating area of research. Of particular interest are films whose ends have been functionalized with electron donors or acceptors that can exchange electrons with the electrode surface. In the simplest case, in which no other electrodes are present, electron exchange between the active species and the electrode is well described by the Marcus–Hush type of theories and their modern extensions [24]. The main difference compared to normal electron exchange with a solvated species is the presence of the intervening layer, which impedes electron transfer. The transfer of an electron along a chain molecule belongs to the more general subject of molecular conductance, on which there is a rich literature (see, e.g., [25 – 27]), and which lies outside

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E.P.M. Leiva and W. Schmickler

of this review. In particular, the dependence of the electron-transfer rate on the chain length has been investigated by several groups (e.g., [28]); often, an exponential decay is observed, which is usually expressed in the form: k ∝ exp −βl

(10)

where l is the chain length; the decay constant β is often found to be of the order ˚ −1 ; this value reflects both the electronic properties of the wire and a posof 1 A sible length dependence of the reorganization energy associated with the electron transfer. Since the presence of the chain decreases the reaction rate, it is possible to measure the rate constant over a large range of potentials. This is usually not possible on bare electrodes since the rate becomes too fast at high overpotentials. In fact, the best proofs for the sigmoidal dependence of the rate on the potential, predicted by electron-transfer theories [29] have been obtained on film-covered electrodes.

3.2 Metal–Adsorbate-Metal Systems Adding a second electrode, such as the tip of an STM, to the system greatly increases the possibilities for investigations. A possible configuration, consisting of an electrode and a tip, is shown in Fig. 10. The electro-active centers now serve as an intermediate state for the electron exchange between the two metals. Various mechanisms for the indirect electron exchange have been proposed, and we shall discuss them in turn.

Fig. 10 Basic setup for investigating an adsorbed redox center with the tip of an STM

Theories and Simulations for Electrochemical Nanostructures

19

3.2.1 Two-Step Mechanism Conceptually, the simplest mechanism for electron exchange between two metals and an intermediate consists of two chemical reactions. The overall rate can then be obtained from formal chemical kinetics. In Fig. 10, we denote the rate constant for electron transfer from the electrode to the intermediate by k1 , and for the back reaction by k−1 , and by k2 , k−2 the rates from the intermediate to the tip and back. Under stationary conditions, rate of electron transfer from the metal to the tip is: v=

k1 k2 − k−1 k−2  i ki

(11)

As with all electrochemical reactions, the rate constants depend on the potential. We choose, as our reference potential for the reactant the value, when the electron exchange between the left metal electrode and the reactant is in equilibrium, and denote the deviation from this value by the overpotential η. Under normal experimental conditions, η will be of the order 100 mV, so that we may use the usual Butler–Volmer equation for the potential dependence of the rate constants. For simplicity, we take a value of 1/2 for the transfer coefficient, so that there is a symmetry between the forward and the backward reaction; both theory and experiment give values close to 1/2 for simple electron exchange. Thus we have: k1 = k10 exp

e0 η , 2k B T

k−1 = k10 exp −

e0 η 2k B T

(12)

where e0 is the unit of charge, k B is Boltzmann s constant, and T the temperature. Electron exchange between the reactant and the tip is in equilibrium, when the bias V between tip and electrode is canceled by the overpotential. Therefore, we may write: k2 = k20 exp

e0 (V − η) , 2k B T

k−2 = k20 exp −

e0 (V − η) 2k B T

(13)

Experiments are usually either performed at constant bias V and variable potential η, or at fixed η and variable V . Figure 11 shows calculated current–potential curves corresponding to the former type of experiments. The current shows a maximum when η lies between zero and V ; its position is determined by the condition that the average occupancy of the intermediate state is one half. Therefore, the maximum is at the potential where the faster of the two electron exchanges is in equilibrium. Calculated curves for variable bias are shown in Fig. 12. As may be expected, the rate increases strongly with the bias. Here the two standard rates were set equal, k10 = k20 = 1, so that for a given bias, the optimum value for the overpotential lies at about η = V /2. Electron exchange in solutions generally require thermal activation, usually connected to the reorganization of the solvent. When the electronic coupling is weak, the system will subsequently relax to a new thermal equilibrium, and a real

20

E.P.M. Leiva and W. Schmickler k10 = k20 k20 /k10 = 0.1 k20 /k10 = 10

rate

1.0

0.5

0.0

–0.1

0.0 /V

0.1

Fig. 11 Calculated current–potential curves at a constant bias; the standard rate for exchange between the electrode and the intermediate was set to k10 = 1

η η η = –0.05 V

bias v/volt Fig. 12 Calculated current-bias curves at a constant overpotential; the standard rates were set to k10 = k20 = 1

intermediate state is formed. Then the mechanism discussed above will prevail. However, if the electronic coupling is strong another electron transfer may occur before relaxation; the corresponding mechanisms will be considered below. 3.2.2 Resonant Transition When thermal relaxation is slower than electron transfer, the reactant can serve as a virtual intermediate state. In this section we discuss the basic mechanism. To be specific, we consider the current for electron transfer from the electrode to the tip. In contrast to ordinary electron-transfer reactions, the electronic energy need not be conserved in the process. If the transferring electron couples to vibrations localized in the reactant, it can transfer energy to them; this constitutes an inelastic

Theories and Simulations for Electrochemical Nanostructures

21

exchange, in contrast to elastic processes where the electronic energy is conserved. In principle, the electron can also pick up energy from an excited vibration, but this process, which is similar to anti-Stokes transitions in Raman scattering, is so unlikely that it can be disregarded. In general, the current associated with the transfer can be written in the form (see Fig. 13): j=

f ()[1 − f (  − e0 V )]T (,   ) ≈



0 −e0 V

T (,   )

(14)

where f () denotes the Fermi–Dirac distribution, V is the bias between the two electrodes, and the Fermi level of the left electrode has been taken as the energy zero [30]. In the approximate version the Fermi–Dirac distributions have been replaced by step functions. The form of the transmission function depends on the mechanism of electron transfer; the process is similar to resonant transitions in solid-state systems [31]. In the simplest case the intermediate state just interacts electronically with the two bulk metals. Due to these interactions, the intermediate state, with energy r , attains a resonance width ⌬ = ⌬1 + ⌬2 , with contributions from both electrodes. In the so-called wide-band approximation the resonance width is independent of the electronic energy ; as the name indicates, this approximation should be valid if the widths of the bands in the two bulk metals, to which the intermediate state couples, is much larger than ⌬. Usually this is a safe approximation, and the transmission function then takes the form of a Lorentz distribution: T (,   ) =

⌬2 δ( −   ) ( − r )2 + ⌬2

(15)

This equation is easily interpreted: The intermediate state serves as a resonance of total width ⌬, and only elastic scattering is allowed, as is indicated by the deltafunction. The same equation has been derived for the conductance of a mono-atomic

Fermi level

ε

Fig. 13 Elementary process of electron transfer from an electrode to a tip

electrode

bias V

ε′

Fermi level

tip

22

E.P.M. Leiva and W. Schmickler

molecular wire [32]. In an electrochemical environment the electron always couples to solvent modes, so that the resonance energy becomes a function of the solvent coordinates qν , where ν labels the solvent modes. These are usually classical, and if they are the only modes with which the electron interacts is sufficient to introduce an explicit dependence r (qν ) into eq. (15) and perform a thermal average over all solvent configurations. The details of this averaging depend on the situation. There are two possibilities: (1) The electron transfer to the acceptor is so fast that there is no electronic equilibrium between the electrode and the reactive center. In this case electron transfer occurs through the empty orbital, and the average is performed over the corresponding solvent configurations. (2) Electron exchange between the electrode and the center is much faster than the exchange with the tip, so that the redox species is in electronic equilibrium with the electrode, and the transfer can either occur from a filled state or through an empty one. We consider the former situation first and return to the other below. The thermal average over the solvent configurations corresponding to an empty center is readily accomplished. The result can be written in the form [30]: Tth (,   ) = ⌫1 ⌫2 δ( −   )



π λk B T

exp

(x − ( − r ))2 1 dx 2 4λk B T x + ⌬2

(16)

and is thus a convolution of the Lorentz distribution with the Marcus-type thermal broadening [1, 33]:

Treorg () =

( − r )2 π exp − λk B T 4λk B T

(17)

Thus, the electronic level of the resonant state is broadened by two effects: The electronic coupling induces the width ⌬, and the interaction with the solvent fluctuations results in a thermal broadening of width (4λkT )1/2 . The electrons move much faster than the solvent; therefore, the electronic energy is conserved, and the transition is elastic. The integral in Eq. (16) can be expressed through the complex error function W(z) = exp(−z 2 ) erfc(−i z) to yield:  π 1/2   −  + i ⌬  r D() = √  W kT λ 2 kT λ

(18)

where  denotes the real part. D() can be considered as a generalization of the redox density of states for electron transfer as defined by Gerischer [34]. With its aid Eq. (16) can be written in the compact form: Tth (,   ) = ⌫1 ⌫2 δ( −   )D()

(19)

Theories and Simulations for Electrochemical Nanostructures

23 Δ = 0.1 eV Δ = 0.01 eV Δ = 0.001 eV

D( )

0.8

0.4

0.0

–0.5

0.0

ε – εr

0.5

Fig. 14 Some examples for the generalized redox density of states D(); the reorganization energy was set to λ = 0.5 eV, and the temperature to T = 293 K

A few typical examples for D() are shown in Fig. 14. The width of the Gaussian is (k B T )1/2 , that of the Lorentzian is ⌬, and the shape of D() is governed by the broader of the two distributions. Quantum modes move on the same timescale as electrons. Therefore, when the transferring electrons couple to vibrations on the reactant, inelastic transitions can occur. As mentioned above, the most likely inelastic process is the excitation of a vibration. The transition function can then be written as a sum over the number of phonons that are excited: T (,   ) =

∞ 

An ()δ( −   − nω)

(20)

n=0

where ω is the frequency of the excited mode. Explicit expressions for the corresponding amplitudes have been given in the literature [30]. Of course, the electron may couple to more than one quantum mode; the corresponding generalization of Eq. (20) is cumbersome, though not difficult. Since the transferring electron must come from an occupied state and go into an empty state, the number of phonons n emitted must obey nω ≤ e0 V (see Fig. 13). Therefore, the number of inelastic channels that are open depends on the bias potential. In principle, this offers the possibility to perform spectroscopy on the quantum modes that couple to the electron transfer by measuring the current as a function of the bias. Every time the bias passes a multiple of ω, a new elastic channel opens, with a corresponding increase in the current. In the second derivative d2 I /dV 2 the opening of a channel will appear as a peak. Figure 15 shows a few calculations exhibiting this effect. The difference between two peaks gives the energy of the emitted photon, and the amplitude indicates the coupling strength. Depending on the magnitude of the latter, a sizable fraction of the current can pass through inelastic channels at high bias voltages.

24

E.P.M. Leiva and W. Schmickler

Fig. 15 Calculated second derivatives of the current as a function of the bias voltage

3.2.3 Adiabatic Limit Kuznetsov and Schmickler [34] have considered the case in which the electron exchange of the reactant with the two metals is adiabatic, so that the electronic system, for a given value of the solvent coordinates, is in equilibrium. If only classical solvent modes are coupled to the transfer, they can be represented by a single effective solvent coordinate q [35]. It is convenient to normalize q in such a way that q = 0 corresponds to the oxidized and q = 1 to the reduced state. In the adiabatic limit, for each value of q, there is a constant flux of electrons from one metal to the other, resulting in an average occupation nr of the intermediate orbital, which is given by: 1 nr = π



E el F −∞

⌬1 1 dω + 2 2 (ω − ˜ (q)) + ⌬ π



tip

EF −∞

⌬!2 dω (ω − ˜ (q))2 + ⌬2

(21)

where ˜ (q) = r − 2λq is the electronic energy of the adsorbate level as a function tip of the solvent coordinate. E el F is the Fermi level of the electrode and E F that of the tip. The rate of electrons passing from the electrode to the tip is then given by [30]: k(q) =

1 π



E el F tip EF

⌬1 ⌬2 dω (ω − ˜ (q))2 + ⌬2

(22)

The effective potential-energy surfaces for the system are markedly affected by the presence of the tip. Figure 16 shows some examples for various values of the couplings ⌬1 and ⌬2 for the case where the intermediate is in equilibrium with the left electrode. In contrast to the Marcus theory for simple electron transfer, in which the adiabatic potential energy curves are composed of two parabolic sections, the activation region is markedly broadened by the interaction with the tip. The corresponding

Fig. 16 Potential–energy curves for the case where the intermediate is in equilibrium with the left electrode. System parameters: λ = 0.6 eV; Vb = 0.2 V. Full curve: ⌬1 = ⌬2 = 0.05 eV; short dashes: ⌬1 = ⌬2 = 0.01 eV; long dashes: ⌬1 = ⌬2 = 0.001 eV

25

U(q)/λ

Theories and Simulations for Electrochemical Nanostructures

–

Fig. 17 Occupation probability of the intermediate for the case depicted in Fig. 16. System parameters: Full curve: ⌬1 = ⌬2 = 0.05 eV; long dashes: ⌬1 = ⌬2 = 0.01 eV; short dashes: ⌬1 = ⌬2 = 0.001 eV

occupation probabilities nr are shown in Fig. 17. For the chosen parameters, there is an extended saddle-point region in which the occupation probability is close to 1/2. The rate of electron exchange can either be determined by performing a thermal average over Eq. (22) or by stochastic molecular dynamics; the latter was the route chosen by Kuznetsov and Schmickler [34]. Unfortunately, the relationships between the current and the bias, or the current and the potential, are qualitatively similar to those obtained from the simple two-step mechanism discussed above. As an example we show the relation between the current and the overpotential with respect to the left electrode, calculated at constant bias (see Fig. 18). However, the exact shape of such current-overpotential curves depends on the energy of reorganization λ for electron transfer to the intermediate state. This can be used to extract λ from experimental data. This is shown in Fig. 19, where experimental data from Tao [37], which were obtained from doped protoporphyrins films adsorbed on highlyoriented graphite electrodes at a constant bias of 50 mV, are compared with calculated

26

E.P.M. Leiva and W. Schmickler

Fig. 18 Current as a function of the overpotential η with respect to the left electrode. System parameters: ⌬1 = ⌬2 = 0.01 eV; Vb = 0.1 V. (•) λ = 0.2 eV; () λ = 0.4 eV; (×) λ = 0.6 eV. The currents have been normalized such that the maximum current is unity

–

–

Fig. 19 Current as a function of the overpotential. System parameters: ⌬1 = 0.01 V, ⌬2 = 0.001 V, Vb = 0.05 V. Full line: λ = 0.6 eV; dashed line: λ = 0.4 eV; dotted line: λ = 0.2 eV. The points are the experimental values from Tao [36]

–

–

–

η/V

curves. As can be seen, the experimental data can be fitted to a reorganization energy of the order of λ = 0.4 − 0.6 eV. However, the same data can also be explained by assuming a nonadiabatic process [37].

3.3 Two Intermediate States Progress in nanofabrication has made it possible to study electron exchange between two electrodes covered by electroactive adsorbate layers (see Fig. 20). Again, the simplest mechanism consists of normal chemical reactions, in this case consisting of two electrochemical and one chemical step. If the active sites are not fixed, diffusion may also play a role. For experimental details and interpretation in terms of a series of reactions we refer to [38, 39, 40]. We focus here on the exchange through virtual intermediates, or superexchange. First we discuss the elementary act, and then interpret a specific example.

Theories and Simulations for Electrochemical Nanostructures

27

Fig. 20 Electron exchange between two electrodes mediated by two adsorbate films with active sites

3.3.1 Electron Exchange via Two Bridge States The electronic interactions are now governed by three terms: the resonance widths ⌬1 and ⌬2 for electron exchange of the left film with the left electrode and of the right film with the right electrode, and by the matrix element V12 for exchange between the two films. Similarly, there are two energies of reorganization λ1 and λ2 for the two electroactive species; in addition, there can be an overlap λ12 between the two solvation spheres. We focus on the basic case, in which the overlap between the solvation spheres is negligible, and in which the coupling V12 between the two sites is smaller than the coupling ⌬1 and ⌬2 . A fuller treatment has been given by Schmickler [41]. Under the conditions given above, the current from the left electrode to the right can be written in the form: 2π e0 |V12 |2 if = 



0 −e0 Vb

d D1 ()D2 ()

(23)

where the redox densities of states have been given in eq. (18 ). Equation (23) is easily interpreted: Only electronic levels between the two Fermi levels contribute; the contribution of each energy level is proportional to the overlap in the density of states of the two participating states and to their coupling. With two redox systems participating, there are a fair number of system parameters, and various shapes of current-potential curves are possible; some particular cases have been discussed in the literature [41]. We restrict our discussion here to the case where the two redox systems are equal, because this is a case which has been investigated both experimentally and theoretically. 3.3.2 Electron Exchange via Two Equal Reactants The groups of Rampi and Whitesides have conducted numerous experimental investigations into indirect electron exchange between two metals in close contact. Here

28

E.P.M. Leiva and W. Schmickler

we consider in greater detail their work with two chemically equal intermediate states, and interpret this in the light of the previously presented model. The basic system is thus as shown in Fig. 20, where the adsorbates consisted of monolayers of [Ru(NH3 )5 (NC5 H4 CH2 NHCO(CH2 )10 SH][PF6 ] Compared with the general results of the previous section, there are some modifications. First, since the intermediate states are well separated from the metal, the level widths ⌬1 and ⌬2 are small compared to the thermal broadening, and can hence be neglected in the redox density of states. Further, the experimental data are consistent with the assumption, that the Rucenters are in electronic equilibrium with the metals on which they are attached. If we assume that the current flows from the left to the right electrode, this means that the electrons are transferred from occupied states on the left electrode to empty states on the right electrode. Therefore, D1 () in Eq. (23) must be replaced by the density of occupied, or reduced, levels, which is [29, 33]:  =

1 Dred ()

4π λk B T

1/2 exp −

(λ +  − e0 η1 )2 4λk B T

(24)

where η1 is the deviation of the potential of the right electrode from the standard equilibrium potential for electron exchange with the adsorbed species. Similarly, D1 () must be replaced by the density of empty, or oxidized, levels, which is:  2 () Dox

=

4π λk B T

1/2 exp −

(λ −  − e0 η2 )2 4λk B T

(25)

The current exchanged between the two metals is then proportional over that part of the product that lies between the two Fermi levels: i∝

E 2F E 1F

D p ()d =

E 2F E 1F

1 2 Dred () × Dox () d

(26)

The situation is depicted in Fig. 21. Two kinds of experiments have been performed: In one type the potential of the left electrode was kept constant, and the bias was increased. In Fig. 21 this corresponds to lowering the Fermi level of the right electrode. Obviously, the current will increase with the bias and tend to a constant value, once the maximum of the product D p () lies between the two Fermi levels. This has indeed been observed (see Fig. 22). The second type is more interesting: here the bias is kept constant at a small value, while the electrode potential is varied. This amount to shifting D p () with respect to the two Fermi levels, so that the current essentially maps out D p (). This makes it possible to obtain the energy of reorganization λ from the current–potential curves. A corresponding plot is shown in Fig. 23, which shows that the experimental data can be fitted with a value of λ = 0.4 eV, which is of a reasonable order of magnitude for a redox species attached to an adsorbate.

Theories and Simulations for Electrochemical Nanostructures (b)

(a)

electronic energy

29

2

1

Dox

Dox

1

2 Dred × Dox

EF

EF 1

2

Dred

Dred

Fig. 21 Indirect electron exchange via two identical species

2.00e-04

current/A

Fig. 22 Currents at both electrodes as a function of the potential of electrode 2; the potential of the first electrode was kept constant at −0.2 V

0.0

–2.00e-04 –0.2

1.1 0.9

normalized current

Fig. 23 Comparison between experimental and theoretical data. In the calculations, λ = 0.4 eV

0.2

0.0

φ/ V vs Ag/AgCl

0.7 0.5 0.3 0.1 –0.1 –0.4

–0.2

0.0

0.2

φ/V

0.4

0.6

30

E.P.M. Leiva and W. Schmickler

However, even though this explanation in terms of the theory is consistent, and the experimental data fit well, an explanation in terms of a two-step mechanism, similar to the one discussed in Section 3.2.1, cannot be ruled out at this stage.

4 Conclusion As mentioned in the introduction, electrochemistry, at least in principle, offers excellent opportunities for the creation of nanostructures. As is evidenced by two recent issues of surface science [42, 43] devoted to this topic, or by the recent work of the Wandlowski group [44], there is ample experimental activity in this area. Of the related theoretical work we have focused here on the two aspects on which most work has been done: the simulation of metal nanostructures and theories of electron transfer through adsorbates. The former work seems quite mature, and has been successful in explaining the properties of several types of structures. In particular, it has explained the unusual stability of some clusters, which had erroneously been attributed to quantum confinement [45], by alloy formation. This is especially important, since electrochemical scanning probe techniques do not give information on the chemical nature of atom that is observed and do not allow one to tell if an observed metal structure is pure or alloyed. Electron transfer through electrochemical structures is a more speculative topic. The theories are quite advanced, and there are good experiments, but it is difficult to decide, what the electron-transfer mechanism is specific situations is. Often the data can be explained by more than one model. Besides the topics that we have treated here, there are theories and models for other electrochemical nanostructures such as steps [46, 47] and islands [48] or nanowires [49, 50]. However, we have not included them here because of restrictions of space, and because it would have made this review too inhomogeneous. Acknowledgments W.S. acknowledges financial support by the Deutsche Forschungsgemeinschaft. E.P.M.L. acknowledges financial support from CONICET, Agencia C´ordoba Ciencia, Secyt U.N.C., Program BID 1201/OC-AR PICT No. 06-12485.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

R. A. Marcus, J. Chem. Phys. 24 (1956) 966. N. S. Hush, J. Chem. Phys. 28 (1958) 962. S. M. Foiles, M. I. Baskes, M. S. Daw, Phys. Rev. B 33 (1986) 7983. G.E. Engelmann, J. Ziegler, D.M. Kolb, Surf. Sci. Lett 401 (1998) L420. D.M. Kolb, F.C. Simeone, Electrochim. Acta 50 (2005) 2989. D.M. Kolb, R. Ullmann and J.C. Ziegler, Electrochim. Acta 43 (1998) 2751. U. Landman, W.D. Luedtke, N.A. Burnham, R.J. Colton, Science 248 (1990) 454. M.G. Del P´opolo, E.P.M. Leiva, M.M. Mariscal, W. Schmickler, Surf. Sci. 597 (2005) 133. M.M. Mariscal, C.F. Narambuena , M.G. Del Popolo, E. P. M. Leiva, Nanotechnology 16 (2005) 974. 10. N.B. Luque, E.P.M. Leiva, Electrochimica Acta 50 (2005) 3161.

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11. M.G. Del P´opolo, E.P.M. Leiva, H. Kleine, J. Meier, U. Stimming, M. Mariscal, W. Schmickler, Appl. Phys. Lett. 81 (2002) 2635. 12. M. Mariscal, W. Schmickler, J. Electroanal. Chem. 582 (2005) 64. 13. D.M. Kolb, M. Przasnyski, H. Gerischer, J. Electroanal. Chem. 54, (1974) 25 . 14. G.E. Engelmann, J.C. Ziegler, D.M. Kolb, J. Electrochem. Soc. 45 (1998) L33. 15. R. Ullman, PhD. Thesis, Fakult¨at f¨ur Naturwissenchaften der Universit¨at Ulm (1997). 16. J.C. Ziegler, PhD Thesis, Fakult¨at f¨ur Naturwissenschaften der Universit¨at Ulm (2000). 17. D.M. Kolb, G.E. Engelmann, J.C. Ziegler, Solid State Ionics, 131 (2000) 69. 18. U. Landman, W.D. Luedtke, Scanning tunnelling microscopy, Chapter 3, Springer Verlag, (1993). 19. S.M. Foiles, M.I. Baskes, M.S. Daw, Phys. Rev. B 33 (1986) 7983. 20. R. Schuster, V. Kirchner, X.H. Xia, A.M. Bittner, G. Ertl, Phys. Rev. Lett. 80 (1998) 5599. 21. T. Solomun, and W. Kautek, Electrochimica Acta 47 (2001) 679. 22. X.H. Xia, R. Schuster, V. Kirchner and G. Ertl, J. Electroanal. Chem. 461 (1999) 102. 23. C. S´anchez, E.P.M. Leiva, J. Electroanal. Chem 458 (1998) 183. 24. C.E.D. Chidsey, Science 251 (1991) 919. 25. Molecular Electronics – Science and Technology, edited by A. Aviram and M. Ratner, Ann. N.Y. Acad. Sci. 852 (1998). 26. S. Roth, C. Joachim, Atomic and Molecular Wires, Kluwer, Dordrecht (1997). 27. Molecular Devices, edited by F. L. Carter, Marcel Decker, N.Y. (1982). 28. J.F. Smalley, S.W. Feldberg, C.E.D. Chidsey, M.R. Lindford, M.D. Newton, Yi-Ping Liu, J. Phys. Chem 99 (1995) 13149. 29. W. Schmickler, Interfacial Electrochemistry, Oxford University Press, New York, 1996. 30. W. Schmickler, Surf. Sci. 295 (1993) 43. 31. N.S. Wingreen, K.J. Jacobsen, J.W. Wilkins, Phys. Rev. Lett. 61 (1988) 1396; Phys. Rev. B 40 (1989) 11834. 32. L.E. Hall, J.R. Reimers, N.S. Hush, K. Silverbrook, J. Chem. Phys. 112 (2000) 1510. 33. H. Gerischer, Z. Phys. Chem. NF 6 (1960) 223. 34. A.N. Kuznetsov, W. Schmickler, Chem. Phys. 282 (2002) 371. 35. M.T.M. Koper, W. Schmickler, A Unified Model for Electron and Ion Transfer Reactions on Metal Electrodes, in: Frontiers of Electrochemistry, ed. by J. Lipkowski and P.N. Ross, VCH Publishers (1998). 36. N. Tao, Phys. Rev. Lett. 76 (1996) 4066. 37. W. Schmickler, N. Tao, Electrochim. Acta 42 (1997) 2809. 38. E, Tran, M.A. Rampi, G.M. Whitesides, Angew. Chem. Int. Ed. 43 (2004) 3835. 39. M.L. Chabinyc, X. Chen, R.E. Holmlin, H.O. Jacobs, H. Skulason, C. D. Frisbie, V. Mujica, M.A. Ratner, M. A., Rampi, G.M. Whitesides, J. Am. Chem. Soc. 124 (2002) 11730. 40. C. Grave, E. Tran, P. Samor, G. M. Whitesides, and M. A. Rampi, Synthetic Metals 147 (2004) 11. 41. W. Schmickler, Chem. Phys. 289 (2003) 349. 42. Surface Science 573 (2004). 43. Surface Science 597 (2005). 44. Z. Li, B. Han, L.J. Wan, T. Wandlowski, Langmuir 21 (2005) 6915. 45. D. M. Kolb, G. E. Engelmann, J. C. Ziegler, Angewandte Chemie, Int. Ed. 39 (2000) 1123. 46. H. Ibach, W. Schmickler, Phys. Rev. Lett., 91 (2003) 016106. 47. M. Giesen, H. Ibach, W. Schmickler, Surf. Sci. 573 (2004) 24. 48. M. Giesen Progr. Surf. Sci. 68 1 (2001). 49. E. Leiva, P. V´elez, C. Sanchez, W. Schmickler, subm. to Phys. Rev. B74 (2006) 035422. 50. M.G. Del P´opolo, PhD. Thesis, Facultad de Ciencias Qu´ımicas de la Universidad Nacional de C´ordoba (2002).

SPM Techniques O.M. Magnussen

1 Introduction Scanning probe microscopy (SPM) techniques are of central importance to nanoscience and nanotechnology. They allow characterization of the local structure and properties of surfaces and interfaces as well as surface modification on the micro- to subnanometer scale, opening up the possibility to perform physical, chemical, and biological experiments on individual nanoscale objects. Contrary to many surface science and electron microscopy methods, SPM techniques are not restricted to vacuum conditions, but can be performed in gaseous and liquid environment, including electrolyte solutions. They have therefore become a major, indispensable tool for the in situ study of electrochemical interfaces and interface processes and play an important role in the development of electrochemical surfaceand nanoscience. All SPMs are based on a common, simple principle (Fig. 1a): the sample surface is approached by a probe, typically a cone-shaped or pyramidal tip with an apex of (sub) micrometer dimensions, which interacts with the sample by a distancedependent, local interaction. Depending on the SPM technique this interaction is different in nature, for example, electrical, magnetic, mechanical, chemical, and optical. It provides a signal (e.g., an electric signal or a force), which is measured by a sensor, compared with a setpoint value, and used to control the probe position in z direction via a mechanical actuator. Sensor, control electronics, and actuator thus form a negative feedback loop that keeps the probe-sample distance constant. By scanning a rectangular area of the sample line by line and simultaneously recording the mechanical motion of the probe, a three-dimensional (3D) “image” of the surface can be generated. Technically, this 3D motion is usually performed by applying appropriate voltages to piezoelectric actuators that move the probe and sample

O.M. Magnussen (B) Institut f¨ur Experimentelle und Angewandte Physik, Christian-Albrechts-Universit¨at zu Kiel, 24098 Kiel, Germany e-mail: [email protected]

P. Schmuki, S. Virtanen (eds.), Electrochemistry at the Nanoscale, Nanostructure Science and Technology, DOI 10.1007/978-0-387-73582-5 2,  C Springer Science+Business Media, LLC 2009

33

34 Fig. 1 Schematic illustration of (a) the basic principle of SPM measurements and (b) the main operating modes, that is, operation at constant current (STM) or constant force (AFM), respectively, (left) and operation at constant height (right)

O.M. Magnussen

a x, y

z

z

b z

z

s

s

relative to each other. To suppress mechanical vibrations and thermally induced drift motion, a major problem in any high-resolution microscopy, compact setups with high mechanical stiffness are used. A detailed treatment of the theoretical underpinnings and experimental realization of the most common scanning probe methods can be found in several textbooks on SPM [1–4]. The microscopic resolution of an SPM technique is determined by the effective size of the interacting areas on tip and sample, which, in turn, depends strongly on the variation of the interaction with probe-sample distance. In the case of very pronounced distance dependence, the measured signal can be dominated by the interaction with the outmost atom of the probe, resulting in true atomic resolution (see below). In general, the generated image is a convolution of probe and sample shape and can substantially deviate from the real sample topography if the surface exhibits features that are sharper than the tip apex (Fig. 1a, black arrows). This can cause characteristic artifacts, such as broadening of steep steps and hillocks, problems in imaging pores and crevices, and multiple imaging of prominent features with probes that end in several tips. For this reason, preparation of sharp probes with well-defined shape and the use of sufficiently smooth sample surfaces are important prerequisites for SPM experiments. As shown above, an SPM image is a map of local properties rather than merely an accurate reproduction of the surface topography, that is, the positions of the ion cores. This is a major strength of SPM techniques and has been extensively used for the characterization of nanoscale structures. It allows, for example, to distinguish areas of different chemical composition or electronic properties (see Fig. 1a, white arrow), such as in alloys (see Section 2.2), coblock polymers, or standing electron waves as in the famous quantum corral structures [5]. An even more comprehensive sample characterization can be obtained by recording several signals in parallel in an SPM experiment. For example, in scanning near-field optical microscopy (SNOM;

SPM Techniques

35

see also Section 4), a force signal is typically used to keep the probe-sample distance constant and to record the sample topography, while simultaneously measuring the local optical properties [2]. SPM is a scanning technique, where the image is generated by sequential recording of data points. Its temporal resolution is therefore limited by the maximum scanning speed, which in turn is determined by the bandwidth of the signal acquisition and the requirements of the control electronics for stable negative feedback operation. In the most common mode of operation (called “constant current” and “constant force” mode in scanning tunneling microscopy (STM) and atomic force microscopy (AFM), respectively) the signal s is kept constant during the scan and the height z of the probe is recorded (Fig. 1b, left panel). This requires the feedback to be sufficiently fast to follow the contours of the surface. Usually, only scanning speeds up to several hundred nanometers (nm) per second are possible in this mode, since the limiting frequency of the feedback loop has to be lower than the lowest mechanical resonance frequency of the SPM (typically several kHz) for stable feedback. Higher image-acquisition rates can be obtained in the so-called “constant height” mode (Fig. 1b, right panel), where the time constant of the feedback loop is much lower than the fluctuations in the signal, caused by the spatial variations in probe-sample distance during scanning, and only the average height of the probe with respect to the surface is kept constant. In this mode the image is generated from the fluctuations in the signal s, which often provides a good lateral contrast, but is more difficult to interpret quantitatively. The main application of “constant height” mode SPM is the study of atomic-scale surface dynamics (see Section 2.3). Imageacquisition rates in the video range and above have been obtained by this method [6–10]. Many SPM techniques can be readily applied in situ in electrochemical environment. Obviously, the presence of the electrolyte medium between sample and probe alters their mutual interactions and in turn the SPM signals, as will be discussed below for electrochemical STM and AFM. If electrical signals are measured, the probe has to be treated as an additional electrode (see Section 2.1). For operation in solution usually a vertical setup with the sample placed in a small electrochemical cell (often formed by a Teflon ring pressed on the sample surface) and the probe entering from the top is used. Special attention has to be paid to the employed probes, which have to be stable in this environment against modification or corrosion by chemical reactions (see below). Furthermore, various other technical problems caused by the presence of the electrolyte have to be addressed, for example, the protection of piezo elements and other electronic components against condensation of moisture, which can cause unwanted voltage fluctuations. The following chapter focuses on STM and AFM, the most important varieties of scanning probe microscopy. In addition, some other SPM techniques relevant to electrochemistry will be briefly treated, followed by a discussion of nanostructuring methods based on electrochemical SPM. More detailed overviews on the application of SPM techniques for in situ electrochemical studies are given in several previous reviews [11–19].

36

O.M. Magnussen

2 Electrochemical STM 2.1 Principle of Operation and Experimental Considerations STM is the oldest SPM technique and still offers the highest spatial resolution of all SPMs. After its invention by Binnig and Rohrer [20], it was first operated under ultrahigh vacuum (UHV) conditions, but applied to studies in liquid environment only a few years later [21]. In STM, a conductive sample is scanned with a very sharp metallic tip (usually an etched W or PtIr wire) kept at nm distances. Due to quantum mechanical tunneling of electrons a tunnel current It flows between the tip and sample, if a voltage Ubias is applied. The high resolution of STM stems from the steep exponential decay of It with increasing tip-sample distance ⌬z, which in the most simple 1D model is (for small Ubias ) approximately: It ∝ Ubias · exp(−A ·



¯ · ⌬z) ⌽

√ ¯ is the effective height of the energy ˚ −1 and ⌽ where A ≡ 2 · 2m e / ≈ 1 eV −1/2 A ˚ resulting in barrier for the tunneling electrons. Typical distances ⌬z are 5–20 A, tunnel currents in the pA to nA range. Since the effective barrier height in the tunnel ˚ changes It by an order of regime is typically several eV, a change of ⌬z by 1 A magnitude. Hence, the tunnel current can be effectively restricted to the apex of atomically sharp protrusions (“microtips”) at the very end of the STM tip, even if the overall radius of tip curvature is much larger (typically more than several hundred nm). This is the basis of the capability of STM to resolve individual atoms at the surfaces of metallic or semiconducting substrates. Meso-scale STM images recorded in constant current mode reflect the substrate topography, whereas atomicresolution imaging requires a more precise treatment (see Section 2.2). The tunnel barrier can be formed by a vacuum, gas, or (nonmetallic) liquid phase, that is, also an electrolyte solution. However, in the latter case, the STM tip has to be considered as an additional electrode, as illustrated schematically in Fig. 2. This results (i) in faradayic currents If,tip due to electrochemical reactions at the tip surface and (ii) a contribution to the tip capacity Ct caused by the electrochemical

CE Fig. 2 Schematic illustration of the electric configuration of in situ STM, showing the tunnel tip and working (WE), reference (RE), and counter (CE) electrode, as well as relevant voltages and currents (see text). In addition, the tip coating is indicated in black

If,sample

RE tip

ISECM It

WE

Ut

If,tip Ubias

Us

SPM Techniques

37

double layer of the tip, which both interfere with the STM measurement: First, electrochemical currents at the tip have to be largely suppressed, since only the sum of tunnel and electrochemical current It + If,tip can be measured. Stable STM operation is only possible if the tunnel current is the dominant contribution, that is, It > If,tip . Second, the noise in the high-gain current–voltage converter used to measure the tip current increases with increasing input impedance. For an optimized signal-tonoise ratio, Ct should therefore be minimized, in particular for studies at low tunnel current or high recording speeds. Both If,tip and Ct can be drastically reduced by coating the tip with an electric insulator, leaving only a ␮m-sized area at the tip apex uncovered. The coating material should exhibit a high chemical stability in the electrolyte solution, to avoid contamination of the sample surface. In practice, Apiezon wax, polymer coatings, or electrophoretic paints are the most commonly employed, allowing routine preparation of tips, where If,tip is reduce below 10 pA and Ct to a few pF [22, 23]. In addition, If,tip can be lowered further by keeping the tip potential in the doublelayer regime. This also prohibits adverse structural changes in the tip during the measurements due to electrochemical reactions, such as oxidation, dissolution, or deposition. It requires that not only the potential Us of the sample (working electrode), but also the tip potential Ut is controlled with respect to a reference electrode, which is accomplished by a bipotentiostatic electronic setup with a design adapted to the rather different current ranges of tip (pA to nA) and sample (typically ≥␮A). During changes of the sample potential Us , which is common in in situ electrochemical studies, either the tip bias Ubias or the tip potential Ut can be kept constant. The first mode ensures constant tunnel conditions but may require limiting the accessible range of Us to maintain Ut in the double-layer regime of the tip. In the second mode, the electrochemical conditions at the tip, and consequently If,tip . are independent of Us . The variation of Ubias in this mode usually does not have a strong effect on the STM imaging of metal substrates, where the dependence on Ubias is weak. However, for in situ STM studies of semiconductors, where both tunneling and electrochemical conditions have to be considered, the choice of Ut may be difficult and potentials that allow stable imaging cannot always be found [24, 25]. The electrochemical reactions at tip and sample can also be coupled, if a species generated at one of the electrodes partakes in a reaction at the other electrode (Fig. 2, dashed arrow). This is the basis of scanning electrochemical microscopy (SECM, see Section 4) as well as of some SPM-based electrochemical nanostructuring methods. Due to the strong exponential distance dependence of It , this current (ISECM ) becomes dominant if the tip is withdrawn by a few nm only. This allows combined experiments where the electrode structure is characterized microscopically by STM imaging, and the same tip is used subsequently in an SECM mode to measure the local electrochemical reactivity [26, 27]. Inversely, the presence of the tip also restricts mass transport to the surface, resulting in reduced reaction rates (e.g., considerably lower deposition rates, see below) in the surface area imaged by the scanning tip. Furthermore, due to the small tip-sample distance, the local electrochemical behavior of the sample may be distorted by the presence of the tip.

38

O.M. Magnussen

While such tip effects are unwanted in in situ STM studies of the electrode surface structure, they are of great importance for in situ nanostructuring and will be discussed in more detail in Section 5.

2.2 High-Resolution In Situ Studies of Electrode Surface Structure STM owns its popularity in no small part to the spectacular atomic-scale images of a wide variety of surface and adsorbate structures obtained by it in the last 25 years. This capability has been of tremendous importance for studies of electrochemical interfaces, where most traditional surface-science methods (e.g., electron diffraction) cannot be employed. The demonstration of in situ atomic-resolution imaging of graphite [21, 28] and metal electrodes [29, 30] and the following extensive applications of this technique [14, 15] promoted significantly the development of electrochemical surface science. Up to now, STM is the most widely used in situ method for the atomic-resolution characterization of the electrode surface structure. The examples presented in Fig. 3 illustrate the capability of in situ STM for true atomic resolution. As visible in Fig. 3a, where a reconstructed Au(111) electrode surface is shown, the atomic lattice at the surface is fully resolved, including the small lateral and vertical modulation in the position of the Au surface atoms caused by the surface reconstruction. The variation of the positions within the unit cell of ˚ in vertical the surface reconstruction (indicated by rectangular box) is only ≈0.2 A ˚ within the surface [31]. Similar images have been obtained on direction and ≈0.5 A various single-crystal surfaces of the coinage metals and of many transition metals (e.g., Pt, Ir, Rh, Pd, and Ni) as well as on some semiconductor surfaces [14, 15]. As an example of the latter, an image of hydrogen-terminated Si(111) in NaOH solution is shown in Fig. 3b [25]. In this image, not only the (1 × 1) Si–H lattice, but also individual Si–OH are discernible (manifesting as protrusions, surrounded by an apparent depression), demonstrating clearly that individual surface atoms can be resolved by in situ STM. To understand and correctly interpret such images the imaging mechanism of STM has to be considered in more detail. As illustrated in the energy diagram in Fig. 4, in the case of a negatively biased sample, electrons tunnel elastically through the barrier from an occupied electronic state in the sample to an empty state in the tip. Inversely, electrons tunnel from occupied tip states into empty sample states for positive sample bias. Although all electrons in the energy window defined by Ubias participate, the strongest contribution comes from electrons near the Fermi level εF , for which the tunnel barrier is lowest. According to the standard model of the STM by Tersoff and Hamann [32], where the tunnel current is calculated by perturbation theory for a spherical tip with s-type wave functions, the tip follows in constant current mode lines of constant local density of states (LDOS; Ds (r, ε F )) of the sample at the Fermi level. On metal surfaces, the contours of Ds (r, ε F ) resemble those of the total electron density, so that images in this simplified interpretation depict the metal ion cores (i.e., the topography). This model seems to provide a reliable description of STM images, if the feature size of the imaged surface structures is

SPM Techniques

39

a

b

c

d 1 2 3

Fig. 3 Atomic-resolution in situ STM images of electrode surfaces. (a) reconstructed Au(111) surface in 0.1 M H2 SO4 solution, exhibiting two pairs of surface-dislocation lines (10 × 10 nm2 , from ref. [192]). (b) Hydrogen-terminated Si(111) in 2 M NaOH (9 × 9 nm2 . Reprinted from ref. [25] with permission by the author. Copyright (1996) by American Physical Society). (c) Pb monolayer on Ag(111) in Pb-containing 0.01 M HClO4 solution, exhibiting a moir´e pattern (18 × 18 nm2 . Reprinted from ref. [38] with permission by the author). (d) Au93 Pd07 (111) alloy surface in 0.1 M H2 SO4 solution, showing Pd monomers, dimers, and trimers (marked by arrows 1, 2, and 3, respectively) which appear more prominent in the image than the Au surface atoms (5.5 × 5.5 nm2 ) [F. Maroun, F. Ozanam, O.M. Magnussen, R.J. Behm, unpublished]. In (a) and (d) the superstructure unit cells are indicated

well above the spatial extension of the electron states of the tip (e.g., for surface reconstructions) and if no substantial chemical interactions between tip and sample occur [4, 33]. Later this approach was generalized by considering p- and d-state tip orbitals [3]. More advanced models consider tip and sample as an interacting system and describing the tunnel event as a scattering process [4, 33, 34]. These latter, numerically very demanding approaches, which include multiple pathways of the tunneling electrons and also may consider inelastic effects, provide the most accurate description of the tunneling junction to date [4, 33].

40 Fig. 4 Energy diagram of the tunnel contact. The local densities of states at tip and sample surfaces are indicated perpendicular to the axis indicating the energy

O.M. Magnussen

f

e f

sample

+ e0Ubias

tip

Resolution of the atomic lattice of close-packed metal surfaces, such as in Fig. 3a, usually requires gap resistances ≤107 ⍀, that is, very small tip-sample distances. The Tersoff–Hamann model is not expected to be applicable under these conditions and indeed cannot explain the observed high atomic corrugations. Modern calcu˚ the mutual chemical interactions result in lations indicate that at distances <5 A, significant deformations of the atoms in tip and sample surface, which contribute ˚ significantly to the corrugations [4, 33, 35]. Upon approaching the tip only 0.5 A closer to the surface, the tunnel junction mechanically collapses (“jump to contact”), resulting in the formation of an electric point contact. The small range of distances (and consequently of It ) where such dynamic enhancement of the corrugation occurs may explain why stable atomic resolution of bare metal surfaces is difficult to achieve. These considerations should also hold for high-resolution imaging of the metal-surface lattice in electrochemical environment, since the electrolyte is largely excluded from the tunnel gap at such small tip-sample distances and at most can contain one water layer (see Section 2.5). This is supported by the experimentally observed corrugations in in situ studies, which do not differ noticeable from those under UHV conditions. However, atomic resolution is generally less reproducibly achieved in situ than in UHV–STM experiments, where various standard methods for preparing a defined tip apex exist (e.g., field evaporation, sputtering, and high field treatment; see ref. [3]). Although electrochemical methods (e.g., electrodeposition on the tip) or controlled mechanical collisions of tip and sample can improve the in situ imaging, the development of well-defined procedures for tip sharpening and cleaning in electrolyte solutions which allow the preparation of well-defined tip states capable of atomic resolution still remains a challenge. The possibility to in situ resolve close-packed metal lattices has been particular important for elucidating the structure of electrodes surface, especially of surface reconstructions [36], and ultrathin metal layers, electrodeposited at over- or underpotentials (see below) [37]. In both cases the interatomic distances or even the inplane symmetry of the metal surface layer(s) often deviate from that of the underlying substrate. This results in an additional long-range periodic structure, where surface atoms occupy different sites of the bulk lattice. The corresponding vertical

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and lateral buckling of the surface lattice are directly visible in the STM images. Examples are uniaxial or 2D dislocation network structures, such as the Au(111) surface reconstruction (Fig. 3a), where these deviations from the bulk lattice parameters are restricted to domain walls in the surface layer (brighter stripes in Fig. 3a), or moir´e pattern that exhibit a more uniform lattice mismatch, as illustrated in Fig. 3c for a Pb monolayer on Ag(111) [38, 39]. By analyzing the surface atom positions with respect to the superstructure lattice, the interatomic distances and angles can ˚ [39–41]. be obtained with significantly increased precision (up to ≈0.01 A) A special case is high-resolution imaging of alloy surfaces, where STM has been shown to be capable of distinguishing chemically different surface atoms (“chemical contrast”) [42]. As demonstrated by Maroun et al. for AuPd(111) electrode surfaces, this is also possible in in situ STM studies, which allows to characterize the structure and distribution of different sites on these heterogeneous surfaces (Fig. 3d) [43]. Imaging with chemical contrast may be a valuable tool to clarify the local reactivity of heterogeneous surfaces in electrocatalysis and corrosion science, where alloy electrodes are of great importance. In the study by Maroun et al., the chemical-contrast STM images of the bimetallic AuPd model catalyst revealed at low Pd content a significantly enhanced surface concentration of Pd monomers (arrow 1) as compared to random distributions, whereas the concentrations of Pd dimers (arrow 2) and trimers (arrow 3) were lowered. By correlation of these structural data with electrochemical and spectroscopic results, critical ensemble sizes for the adsorption of hydrogen and CO, important species in fuel cell reactions, could be identified [43]. One of the earliest and most important applications of high-resolution in situ STM has been the investigation of adsorbates on electrode surfaces. In fact, observations of ordered iodine adlayers on Pt(111) [29] and underpotential deposited (UPD) Cu on Au(111) [30] were the first examples of in situ atomic-resolution imaging on metal electrodes. Since then a large number of systems have been studied, including metal adlayers [14, 15, 37], anion adlayers [14, 15, 44], and various molecular adlayers, ranging from simple inorganic molecules (e.g., CO and CN) to large supramolecular assemblies [14, 15]. In particular, STM has significantly helped to elucidate the lateral ordering within these adlayers, revealing an unexpectedly complex 2D-phase behavior. Simple or high-order commensurate structures as well as uniaxial and 2D incommensurate structures with potential-dependent lattice parameters were observed in these studies. A detailed overview on the structural data obtained by STM as well as other techniques can be found elsewhere [14, 15, 37, 44, 45]. STM images of pure metal adlayer such as Pb on Ag(111) (Fig. 3c), which are strongly electronically coupled to the substrate, can be interpreted in a similar way as images of the metal substrate (see above). However, the interpretation of atomicscale images of nonmetallic adsorbates is not straightforward. As shown by UHV– STM studies and corresponding detailed calculations, maxima in the STM images, especially in images of molecules, not necessarily are located at the positions of atoms and the observed heights of the maxima are not at all related to the adsorbate geometry (and may substantially depend on the tunneling conditions) [34, 46].

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Low-temperature STM studies of isolated adsorbates on metal surfaces revealed that even adsorbates that would seem to have no electronic states in the vicinity of the Fermi level, such as noble gases or water, can provide pronounced contrast. In fact, contributions to the STM images come from the adsorbate as well as the underlying substrate, both perturbed by their mutual interaction [34, 46]. While on substrates that interact weakly with the adsorbate (e.g., graphite) the contribution of the substrate can be neglected, on metal substrates the shift of surface levels by the presence of the adsorbate decreases the contribution of the substrate to It , corresponding to a depression in the STM image. The total shape of the adsorbate is given by the interference of the substrate contribution with the direct contribution of the adsorbate, which would create a bump. In the most common case, the adsorbate has no electronic states close to the Fermi energy and the contributions of the adsorbate result from the broad tails of (usually several) molecular orbital (MO) resonances. For simple atomic adsorbates the apparent height was found to correlate with the atomic polarizability or spatial extension of the dominant orbital, respectively, whereas the orbital energy seems to be less important [34]. STM images of more complex adsorbates, for example, (poly)aromatic molecules, have often been interpreted in terms of the molecules HOMO and LUMO. This interpretation seems too simplistic in the light of modern calculations, which indicate contributions of a large number of MOs to the image and a dependence of the observed shape of the molecule on the adsorption site [4, 34]. In general, only a small influence of tunnel bias on the images is expected for the range of Ubias accessible in in situ measurements in electrochemical environment. However, if electronic states of the adsorbate are located in the energy window defined by Ubias strong resonant tunneling through these states may occur, resulting in pronounced contrast (see Section 2.5). For close-packed adlayers additional complications arise. Here the tip may interact simultaneously with several neighboring adsorbates, resulting in electronic interferences that may strongly affect the image. For this reason, images of dense adlayers depend more strongly on the atomic-scale tip shape than on images of isolated molecules. Due to these ambiguities in the interpretation of STM images, unambiguous clarification of the complex structures at electrochemical interfaces is often not possible by STM alone, but requires complementary techniques. √ √ As a characteristic example, in situ STM images of an ordered “( 7 × 3)” sulfate adlayer on Au(111) are presented in Fig. 5 [47]. This type of adlayer structure exists on many (111) surfaces of fcc metals at potentials positive of a critical value, where it is formed in a sharp first-order phase transition [44]. In the images a prominent maximum, corresponding to the sulfate species, and a second, weaker maximum, which is nowadays attributed to a water species bound via hydrogen bonds, is found per unit cell (see Fig. 5a). The images of the sulfate adlayer depend strongly on the tunnel resistance. At low resistance, that is, small tip-sample distance, the adlayer becomes even largely transparent, and the STM images the underlying substrate lattice (Fig. 5b). This shift in image contrast is gradual, reversible, and has been observed for a number of anionic [29, 47–50] and organic [51] adsorbate systems. It can be employed to determine the positions of the maxima in the superstructure relative to the substrate lattice, allowing clarification of the adsorption site in

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Fig. 5 High-resolution in situ STM images of Au(111) in H2 SO4 solution. (a) Characteristic image of the ordered sulfate adlayer (3.6×4.4 nm2 ). (b) Effect of tip-sample distance on STM image, illustrated by stepping the tunnel resistance twice from 15 M⍀ (top, center, bottom) to 2.5 M⍀ and back (10 × 8.5 nm2 ). (c) Change in STM image upon stepping the potential from 0.68 VSCE (upper part), where the substrate lattice is observed, to the potential regime of the ordered adlayer phase (lower part) at 0.69 VSCE (21 × 12 nm2 , after ref. [47]. Reproduced by permission of The Royal Society of Chemistry)

simple adlayer systems [49]. The same is possible by stepping the potential across the phase transition (Fig. 5c). Since the sulfate adsorbate is disordered and highly mobile in the potential range negative of the ordered phase, only the periodicity of the substrate lattice remains visible in the STM image. The position of the adlattice relative to the substrate atoms can then be obtained by extrapolating the substrate lattice into the range of the image where the superstructure is observed. This and

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other “potentiodynamic” STM experiments utilize the fact that the slow scanning direction (by convention chosen along the vertical direction in the images) also provides a time axis. Modern studies utilize in situ STM to characterize the structure of complex supramolecular assemblies on electrode surfaces with submolecular resolution. Two recent examples of this rapidly progressing field are presented in Fig. 6. The first illustrates lateral organization of molecular species for a bimolecular adsorbate system, a mixed monolayer of a Co phthalocyanine and a Cu tetraphenyl-porphyrin on reconstructed Au(100) in HClO4 solution (Fig. 6a) [52]. The STM images reveal ordering in alternating rows of clearly distinct molecules, which can be attributed to the phthalocyanine (I) and the porphyrin (II) species. An example for vertical as well as lateral organization is shown in Fig. 6b [53, 54]. Here a c(2 × 2) Cl adlayer on a Cu(100) surface provides a template for the ordered adsorption of supramolecular squares (as well as co-adsorbed chainlike oligomers of these molecular units, also visible in the image), formed from bipyridine and Pt ions. Specifically, the squares are oriented parallel to the underlying anion adlattice and can, under optimized preparation conditions, exhibit long-range order. Studies of this type can play an important role in bottom-up approaches for nanostructure formation. Additional control over the molecular organization can in many cases be gained by the applied potential (see below), another advantage of the electrochemical environment. The adlayers shown in Fig. 6 should only be considered as representative examples of the large number of organic adlayer systems that have been studied by in situ STM, which even include biomolecular adsorbates such as functional, self-assembled proteins [55]. The structural characterization of functionalized electrodes afforded by STM greatly assists the interpretation of the electrochemical response of these complex systems.

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Fig. 6 High-resolution in situ STM images of supramolecular adsorbate structures. (a) Mixed Co phthalocyanine/Cu tetraphenyl-porphyrin adlayer on reconstructed Au(100) in 0.1 M HClO4 solution (15 × 15 nm2 . Reprinted from ref. [52] with permission by the author. Copyright by American Chemical Society). (b) Square supramolecular aggregates of bipyridine and Pt ions on a c(2 × 2) Cl adlayer covered Cu(100) surface in HCl solution (20.5 × 20.5 nm2 . Reprinted from ref. [53] with permission by the author. Copyright by Wiley-VCH)

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2.3 Studies of Phase Transitions and Transport on Electrode Surfaces STM not only can image static surface structures, but is also a valuable tool to study surface-dynamic phenomena. Electrochemical interfaces, where phenomena such as adsorption/desorption, surface phase transitions, and surface transport processes can be controlled in a very easy way by the potential, are a particularly rich field for this type of studies. The accessible temporal resolution depends on the image-acquisition rates, which for most STMs usually do not exceed some 10 s. Most in situ STM studies therefore focus on structural changes on the timescale of minutes. An early application of time-resolved in situ STM studies was the investigation of the potential-induced reconstruction of Au single-crystal electrodes, a wellstudied phenomenon in electrochemical surface science [36]. According to studies by variety of ex situ and in situ methods, the Au(111), Au(100), and Au(110) surface reconstructions, found on those surfaces under UHV conditions, are only stable negative of a critical potential that depends on crystallographic orientation and electrolyte composition, whereas at more positive potentials a reversible phase transition to the unreconstructed (1 × 1) surfaces occurs. In situ STM studies have contributed significantly to the understanding of the complex mechanisms of the transitions between reconstructed and unreconstructed surfaces [9, 36, 56–62]. In particular, they have revealed the nucleation and growth mechanisms involved in the formation of the (1 × 1) or the reconstructed phase, respectively, and showed the pronounced influence of long-range mass transport on the kinetics of these transitions. A detailed description of these studies can be found in Ref. [36]. A more recent example of potential-induced structural phase transitions can be found on Pt(111) electrodes covered with electrodeposited mono- and bilayer Au films (Fig. 7) [63]. These films are pseudomorphic to the underlying Pt substrate lattice (i.e., significantly compressed with respect to the Au bulk lattice) at potentials <0.35 VAg/AgCl (Fig. 7a), but undergo a sequence of phase transitions to dislocation network structures with uniaxial and two-dimensionally expanded lattices. As in the case of the Au(111) surface reconstruction (see Fig. 3a), the dislocation lines can be directly observed in the STM images (Fig. 7a and b, dark lines). Specifically, the structural transitions start with the formation of a unidirectionally relaxed lattice (“striped phase”) in the Au bilayer islands (marked as (ii) in Fig. 7a), manifesting as a pattern of dislocation lines (Fig. 7b). With increasing potential, first the formation of a similar “striped phase” in the Au monolayer (marked as (i) in Fig. 7a) and then a transition from the “striped” into a “hex” dislocation network phase in the Au bilayer is found. In all these phases the dislocation line spacing increases continuously with potential, that is, the Au surface density gradually decreases (as also revealed by changes in the island morphology), approaching values close to that in bulk Au(111) planes at the most positive potentials. Upon decreasing the potential, the Au layers are compressed again and a transition back into the pseudomorphic (1 × 1) phase occurs (Fig. 7d). This complex phase behavior can be explained by the reduction of

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Fig. 7 Selected in situ STM images of a series recorded on a 1.3 ML Au deposit on Pt(111) in 0.1 M H2 SO4 solution in the same surface area during a full potential cycle between 0.3 and 0.85 VAg/AgCl . (a) Initial pseudomorphic Au film at 0.3 V, Au monolayer, and bilayer islands are indicated by (i) and (ii), respectively. (b, c) Au film with dislocation network structures (dark lines) at (b) 0.6 V and (c) 0.85 V. (d) Pseudomorphic Au film after returning the potential to 0.30 V (20.5 × 20.5 nm2 . Reprinted from ref. [63]. Copyright (2003) by American Physical Society)

the in-plane stress in the Au surface layer(s) due to the adsorption of anions and the minimization of strain energy in the Au film. The possibility to generate and control a wide range of dislocation networks by potential is of interest for the formation of ordered-metal nanostructures, for which such networks may serve as templates (see Section 2.4). Likewise, STM has been used to study phase transitions in adsorbate layers on electrode surfaces. Although these transitions often occur on timescales of milliseconds, that is, too rapidly for conventional STM studies (see, for example, Fig. 5c), details on the mechanisms of the transition can be observed in selected systems. An example is bipyridine on Au(111) electrodes, which forms various ordered phases

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Fig. 8 Selected in situ STM images of a series showing the potential-induced formation of the ordered bipyridine phase on Au(111) in 0.1 M H2 SO4 solution. The images were recorded (a) at 0.10 and (b–d) at 0.5 VSCE (3×35 nm2 . Reprinted from ref. [64] with permission by the author. Copyright by Elsevier Science)

composed of stacked molecular chains at positive-charge densities. Potential- and temperature-induced transitions in this adsorbate system could be followed directly by in situ STM in a study by Dretschkow et al. [64]. In Fig. 8 selected STM images from a series recorded during the nucleation and growth of the ordered bipyridine phase after an increase in potential from 0.10 (Fig. 8a) to 0.5 VSCE (Fig. 8b–d) are shown, indicating an anisotropic growth along the stacking direction and annealing of defects within the ordered phase. Furthermore, a metastable, low-density adlayer with a different chain direction is found prior to the formation of the stable bipyridine phase (Fig. 8b,c). These microscopic observations provide important details on the nanoscale mechanisms of the structural transitions in the adlayer and are a central prerequisite for a realistic modeling of its kinetic behavior.

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A second major topic of in situ STM studies, related to the surface dynamics of electrochemical interfaces in the double-layer regime, is the investigation of mass transport on electrode surfaces. In early studies, morphological changes, such as the decay of adatom or vacancy islands, were qualitatively studied, revealing a pronounced dependence of transport rates on electrolyte composition and potential [65, 66]. If the transport is limited by surface diffusion the decay rates depend in general on the local environment. Nevertheless, quantitative measurements are possible for special geometric configurations and have been reported for electrochemical systems [67]. A comprehensive, quantitative analysis of the diffusion of adatoms of the electrode metal on the electrode surface has been performed for single crystalline Au, Ag, and Cu in elegant STM studies by Giesen and co-workers as well as other groups, employing two different approaches (see Ref. [68] for a detailed overview). The first method is based on STM observations of monolayer islands (or, alternatively, vacancy islands). By analyzing the island shape, the free energies of steps and kinks can be determined. Furthermore, surface-transport mechanisms can be investigated by measuring the Brownian motion or decay of such islands, observed in long series of sequential STM images. In the second method, fluctuations of steps on the metal surface are studied. These fluctuations manifest as a frizzy appearance of the steps in the STM images and can be attributed to the movement of kinks due to rapid emission, capture, and step edge diffusion of metal adatoms. Quantitative studies employ a one-dimensional (1D) scan mode rather than 2D imaging, where the tip scans continuously along a line across the step(s), resulting in an improved time resolution. Such 1D scanning (“x–t scans”) is a frequently applied trick to increase the time resolution on cost of the spatial information and has also been used to study adsorption and metal-deposition processes [37, 69]. From x–t scans of the step fluctuations one can obtain time correlation functions F(t) that exhibit power laws which are characteristic for the dominant mass-transport mechanism. For example, studies of the close-packed steps of Ag(111) in sulfuric acid solutions indicated that the step fluctuations diverge close to the potential regime of Ag dissolution (Fig. 9) [70]. Based on the scaling behavior of F(t), diffusion along the step edge was suggested as the dominant mechanism at negative potentials, whereas close to dissolution rapid adatom exchange between steps and terraces as well as between terraces and the electrolyte seems to prevail. Furthermore, the corresponding activation energies may be evaluated by temperature-dependent measurements. Direct observations with high time resolution are possible using specialized STMs, capable of image-acquisition rates in the video-frequency range or higher. Crucial elements of such Video-STMs are a very stable mechanical setup and a large bandwidth of the preamplifier for the tunnel current (≥500 kHz). Video-STMs not only allow studies of faster processes, which is particularly important in liquid environment where the available temperature range is limited to a regime, where the thermal motion of most adsorbates is high, but also to obtain large data sets in a few minutes, allowing statistically relevant, quantitative studies. As an example, Video-STM studies of adsorbate diffusion on electrode surfaces – an important, but only marginally investigated elementary step in many electrochemical reactions – are illustrated in Fig. 10 for adsorbed sulfide on Cu(100) in HCl solution [10]. In

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Fig. 9 (a) Time correlation functions F(t) at several potentials, obtained from 1D in situ STM scans on Ag(111) in 0.1 M H2 SO4 solution, and (b) resulting potential dependence of F(t). An example of a 1D scan across five parallel steps, where only the x-direction is a spatial axis (50 nm) and the y-direction represents a time axis (60 s), is shown in the inset (Reprinted from ref. [70] with permission by the author. Copyright by Elsevier Science)

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Fig. 10 In situ Video-STM studies of the diffusion of adsorbed sulfur on Cu(100) in 0.01 M HCl solution. (a) two successive images from a video sequence recorded at −0.32 VSCE at 15 images/s, showing Sad hopping diffusion. (b) Potential dependence of sulfur hopping rates at 296 K and corresponding diffusion barrier, obtained from a statistical analysis of video sequences (Reprinted from ref. [10]. Copyright (2006) by American Physical Society)

this system, isolated Sad occupy positions of the c(2 × 2) Cl adlattice, replacing one of the Clad species. The Sad hopping diffusion to neighboring sites in the Clad lattice is directly observed in the recorded video sequences (Fig. 10a, indicated by arrows). From a detailed statistical analysis of the Sad positions in the frames of a video sequence, the probability p(d) that Sad is displaced by a distance d (in units of the Clad lattice) during the time between successive frames is obtained. By fits of these jump-distribution functions to a simple random-walk model, the Sad hopping

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rate was determined as a function of temperature and electrode potential. Specifically, a strong exponential decrease by an order of magnitude per 100 mV potential increase was found (Fig. 10b). Based on the temperature-dependent data, this could be clearly attributed to a linear potential dependence of the activation energy for Sad hopping (“diffusion barrier”), which in turn can be rationalized by an electrostatic contribution to the Sad adsorption energy caused by the electric field at the interface. The latter is in agreement with thermodynamic considerations and data on Au(100) surface diffusion [67] and of general validity for surface transport at electrochemical interfaces. Hence, it is of considerable importance for understanding the kinetics of electrochemical reactions. Video-STM also allows to directly study the dynamics of nanoscale structures, a topic of obvious relevance to nanoscience. A recent example is the observation of a quasi-collective diffusion of the basic elements of the Au(100) surface reconstruction, five atom wide strings of hexagonally ordered Au, within the surrounding square lattice of the Au surface layer (Fig. 11). Video-STM observations revealed a surprisingly high surface mobility of these “hex” stripes, with rapid displacements perpendicular and along the stripe direction [9, 62]. As an example, the mobile free “hex” stripe visible near the upper, left corner of the first image (marked by arrows; the other stripes in these images are pinned to surface defects) moves by more than 10 nm in only 66 ms. Based on similar quantitative studies as described above [71], the sideway hopping of strings can be attributed to the formation and rapid 1D propagation of lateral distortions (“kinks”) within the strings (also manifest in form of a wiggly appearance of the mobile string). Equivalently, this mechanism of motion can be interpreted as a gliding of surface dislocations through the “hex” string. A similar quasi-collective mechanism as well as 1D diffusion of Au

Fig. 11 Sequence of successive in situ Video-STM images showing the quasi-collective motion of nanoscale “hex” strings on Au(100) in Cl-containing 0.01 M Na2 SO4 solution (18 × 29 nm2 , 15 frame/s video, from ref. [9])

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adatoms along the string edges [9] may contribute to the mass transport along the string, necessary for the motion in string direction.

2.4 Studies of Electrochemical Phase Formation Processes The modification of electrode surfaces by faradayic processes, such as electrochemical deposition, etching, and oxidation, is an area of particular significance to nanoscale electrochemistry. As described in Chapters 6, 7, 8, 9 of this book, these processes are utilized extensively in current scientific and technological applications. In situ studies by scanning probe methods such as STM have helped significantly to elucidate the microscopic mechanism of electrochemical phase formation processes. The main emphasis in this area has been on the initial stages of heteroepitaxial metal electrodeposition, which has been investigated for a large number of different metal deposits and substrates [14, 15, 37, 69, 72–74]. Typical studies focus on clarifying the lattice structure and the surface morphology of the deposit and to rationalize those in terms of the thermodynamic growth mode and kinetic effects (e.g., the rates of nucleation as well as intra- and interlayer transport). In many cases, not only the admetal and the substrate, but also parameters such as overpotential or deposition rate, film thickness, and electrolyte composition were found to influence the growth behavior substantially. As a characteristic example, again ultrathin Au films on Pt(111), discussed already above (see Fig. 7), are chosen. STM studies of the electrochemical growth of these films at large overpotentials reveal nucleation and 2D growth of Au monolayer islands (Fig. 12a), followed by a layer-by-layer growth of the first two Au layers (Fig. 12b and c) and subsequent 3D growth (Fig. 12d), that is, a classical Stranski–Krastanov behavior [73]. While the mono- and bilayer deposit is pseudomorphic to the Pt substrate, the presence of a moir´e pattern on top of the 3D Au islands (see Fig. 12d) indicates a structurally relaxed Au lattice at larger film thickness, again in accordance with a Stranski–Krastanov growth mode. In addition, kinetic effects were found to rule the nucleation of Au islands in the submonolayer regime, determining the equilibrium island density on the surface. Specifically, for (diffusion-limited) deposition from sulfuric acid solution, the nucleation density continuously increases to more positive deposition potentials, resulting in a change by a factor of 40 for a potential increase from 0.2 to 0.5 VSCE . Since at the employed, high overpotentials the deposition rate does not depend on potential and Au desorption can be neglected, these STM observations can be understood using the same concepts of kinetic growth theory that have successfully explained UHV–STM data on MBE metal nucleation and growth. In particular, they point toward a pronounced blocking of Au surface transport by co-adsorbed sulfate. Studies of this type can help to evaluate fundamental similarities as well as differences between electrodeposition and deposition under vacuum conditions, clarifying the influence of the potential and co-adsorbed species (anions, water, etc.) on the growth behavior.

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10 Å Fig. 12 In situ STM images showing (a) submonolayer islands (0.3 ML coverage), (b) a monolayer (1.2 ML coverage), (c) a bilayer (1.8 ML coverage), and (d) a multilayer (3.7 ML coverage) Au deposit on Pt(111). The Au films were formed by electrodeposition in KAuCl4 -containing 0.1 M H2 SO4 + 10−3 M HCl at 0 VSCE (370 × 370 nm2 . Reprinted from ref. [73]. Copyright by Elsevier Science)

At low growth rates, electrodeposition processes can be directly followed by in situ STM. This is illustrated for Ni electrodeposition on Au(111) in Fig. 13 a–d, where nucleation and subsequent 2D growth of second-layer islands on a Ni monolayer deposit are observed, revealing the annealing of structural defects (manifesting as a better-ordered moir´e pattern) during the growth [75]. The possibility of such in situ studies is a clear advantage over UHV–STM studies of MBE processes, where the imaged area is geometrically shaded by the STM tip. As shown explicitly in recent finite-element calculations [76], the local electrodeposition rate under the tip is only slightly lower than that far away from the tip position, provided the diffusion of the metal ions in the electrolyte occurs substantially faster than the charge transfer at the electrode surface. The latter is not a very restrictive condition for electrodeposition processes with slow charge-transfer kinetics, such as Ni, but is difficult to fulfill for systems where the charge transfer is fast. For example,

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Fig. 13 (a–d) Sequence of in situ STM images recorded on Au(111) in 0.1 M Ni sulfate solution in the same surface area (90 × 100 nm2 ). The images show the growth of the Ni deposit at −0.66 VAgAgCl and correspond to a Ni coverage of (a) 1 ML, (b) 1.5 ML, (c) 2 ML, and (d) 2.3 ML. (e) Occupation θ i of the first seven Ni layers as a function of total Ni coverage θ, obtained by quantitative evaluation of series of STM images during Ni electrodeposition from Watts electrolyte (Reprinted from ref. [75]. Copyright (1997) by American Physical Society)

the growth rates observed by in situ STM during Cu electrodeposition from sulfuric acid solution are orders of magnitudes smaller than those expected from electrochemical measurements [69]. This as well as other effects of the tip on the observed process can be probed by significantly expanding the scan range and comparing the previously scanned area with the surrounding surface. From series of STM images recorded during deposition, a comprehensive picture of the growth process can be obtained, including nucleation sites, preferred growth directions, and roughness evolution of the deposit. As a simple example, a quantitative evaluation of the deposit morphology in the series of images obtained for Ni on Au(111) clearly demonstrates the almost-perfect layer-by-layer growth of the first five layers (Fig. 13e). Other in situ STM studies have shown that, similarly as for MBE hetero-epitaxial growth, also in electrochemical environment the structure of ultrathin deposited films can deviate significantly from that of the bulk admetal, in particular on strongly corrugated substrates such as fcc(100) surfaces. A well-known example are Cu deposits on Au(100), where the entire deposit changes at a film thickness >10 layers from a pseudomorphic Cu lattice, resembling a bcc copper phase, to a buckled structure with orthorhombically distorted domains that manifest as a pronounced unidirectional modulation in STM images of these deposits [77, 78]. Of special interest to nanoscience are in situ STM studies that focus on the electrodeposition of nanoscale structures. Electrochemical processes involve a chargetransfer process, which may exhibit a rather different kinetics at different surface sites. Under favorable conditions the discharge of the admetal species may even be limited to specific sites, which then act as a template for the formation of admetal

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nuclei. This offers attractive possibilities for the preparation of nanostructured surfaces. The most popular method and a very common phenomenon in metal-on-metal systems (Fig. 12a) is the decoration of the steps of the substrate on the lower terrace side, resulting in quasi-1D monolayer deposits (i.e., nanowires) [79, 80]. In some cases also 3D nanowires can be formed, for example, for Ni electrodeposited on Ag(111), where in situ STM studies revealed a very selective step decoration at intermediate overpotentials (Fig. 14a) [81]. Also, at higher overpotentials 3D islands on the terraces are formed, whereas at very small overpotentials a 2D film growth is observed. In situ observations of the nanowire growth process indicated a mechanism involving heterogeneous nucleation at a defect in the Ni deposit, created by the underlying step, and a higher growth rate for Ni on Ni as compared to Ni on Ag. Also, other heterogeneities on the electrode surface, such as surface reconstructions, were found to act as templates for the nucleation and growth of the admetal. This is illustrated for submonolayer electrodeposits of Ni and Ru, formed at low overpotentials, which decorate selected sites on the reconstructed Au(111) surface (Fig. 14b,c). For Ru, this selective growth occurs in the fcc areas between the dislocation lines, resulting in a replication of the reconstruction domain pattern (Fig. 14b) [82]. In addition, the opposite phenomenon, decoration of the hcp areas, can be observed, as shown in recent STM studies for Co [83] and for Au–Cd surface alloy growth [84]. In the case of Ni electrodeposition, islands nucleate at bending points (“elbows”) of the dislocation lines, resulting in arrays of monolayer islands on surfaces exhibiting a well-ordered herringbone reconstruction (Fig. 14c) [75, 85, 86]. This nucleation behavior was also found for MBE growth of Ni and other transition metals under UHV conditions [87–89] and attributed to place exchange of Ni adatoms with Au surface atoms at the elbow sites, followed by Ni island nucleation on top [88]. Other possible templates for the electrodeposition of regular nanoscale structures may be dislocation networks on ultrathin metal films (as in Fig. 7) [90]

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Fig. 14 In situ STM images of electrodeposited metal nanostructures, employing surface inhomogeneities as a template. (a) 3D Ni nanowires deposited along steps of the Ag(111) substrate (850 × 850 nm2 . Reprinted from ref. [81]. Copyright (1999) by American Physical Society). (b) Submonolayer Ru monolayer islands deposited selectively in the fcc areas of the reconstructed Au(111) surface (100 × 100 nm2 . Reprinted from ref. [82]. Copyright (1999) by American Physical Society). (c) Decoration of the elbows of the Au(111) reconstruction by electrodeposited Ni (230 × 230 nm2 . Reprinted from ref. [86]. Copyright (1996) by American Physical Society)

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and molecular adlayers [91]. Due to its high resolution in situ STM has been an unrivaled tool for the characterization of such nanostructured metal electrodes. Even more complex electrochemical phase-formation processes, specifically also the deposition of nonmetallic materials, have been studied by in situ STM. Stickney and co-workers have developed electrochemical atomic layer epitaxy (ECALE) of compound semiconductors, where a deposit is formed layer by layer using repetitive, successive adsorption steps (e.g., alternating metal and anion adsorption), and investigated the formation of the first layers by a combination of STM, electrochemical, and ex situ methods [92, 93]. As an example, the structure of CdTe bilayers on Au(111) was found to depend on the sequence of the individual growth steps as well as on the potential [93]. For layers where Te was deposited first, resulting in√a (13√× 13) adlayer structure, the successively deposited Cd layer exhibited a ( 7 × 7)R19◦ (Fig. 15a) and a (3 × 3) structure (Fig. 15b) for Cd deposition at −0.5 and −0.6 VAg/AgCl , respectively. Clarification of such complex deposits usually requires a multimethod approach where STM is complemented by other structuresensitive or spectroscopic techniques. Furthermore, in situ STM studies in nonaqueous electrolytes have been performed, where a much wider range of materials can

Fig. 15 In situ STM images of electrodeposited semiconductors. (a,b) CdTe bilayers deposited by the ECALE method on Au(111) from Cd and Te containing H2 SO4 solutions at (a) −0.5 (20 × 20 nm2 ) and (b) −0.6 VAg/AgCl (10 × 10 nm2 ). Details are given in the text (Reprinted from ref. [93] with permission by the author. Copyright by Elsevier Science). (c,d) Electrodeposits of (c) Ge bilayer islands (150 × 150 nm2 . Reprinted from ref. [95, 96] with permission by the author. Reproduced by permission of the PCCP Owner Societies) and (d) Si mono- and bilayer islands (500 × 500 m2 . Reprinted from ref. [97] with permission by the author. Copyright by American Chemical Society), formed by electrodeposition on Au(111) from ionic liquids

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be electrodeposited, including less-noble metals and semiconductors. Endres et al. have constructed an STM, capable of working in rigorously controlled nonaqueous environments (i.e., at water and O2 contaminations <2 ppm) and applied it to studies of metal and semiconductor deposition from ionic liquids [94–97]. Characteristic images of Ge [95, 96] and Si [97] deposits on Au(111), obtained in situ during deposition, are shown in Fig. 15c and d, respectively, demonstrating that high-quality STM images can also be obtained under these conditions. Dependent on the deposition conditions, the formation of thin epitaxial films starting by 2D island nucleation and growth (Fig. 15c,d) or of 3D nanocrystalline aggregates was observed [95, 96]. Such measurements are very demanding due to the experimental efforts involved in maintaining the required purity of the electrolyte. Studies of electrochemical dissolution and oxidation processes have employed in situ STM in a similar way, that is, have investigated the resulting surface structure on the atomic and mesoscopic scale as well as have directly followed the structural changes during these processes. For example, the microscopic mechanisms underlying the pronounced influence of anionic or organic adsorbates on these processes were revealed by such measurements (see, e.g., ref. [15, 44, 98]). Often, STM studies of the electrodeposition of ultrathin metal films include observations of the dissolution of the admetal, which can provide data on the dissolution mechanisms, the defect density in the deposit, and structural changes in the substrate morphology due to surface alloying. Details on metal dissolution and oxidation studies are given in the chapter on nanoscale corrosion (Chapter 10), where these processes play a central role. More complex phase formation processes, such as ECALE, often involve two or more consecutive steps, which often require a change in electrolyte composition (e.g., introduction/removal of electroactive species or pH changes). Although this can, in principle, be accomplished in an in situ STM experiment by exchanging the electrolyte, the latter often leads to changes in the lateral tip position, making it difficult to directly observe the effect of the exchange by comparing the structural changes in the same surface area. To solve this problem Ammann et al. developed complex microfabricated probes with an integrated STM tip and a surrounding “generator electrode”, whose potential could be independently controlled [99, 100]. This allowed to rapidly generate species for an electrochemical reaction (e.g., metal ions or H3 O+ ) in the electrolyte close to the sample. Since the species are delivered to the electrolyte volume in the immediate vicinity of the tip, they have to diffuse only ≈50 ␮m, resulting in almost immediate initiation of the reaction in the imaged surface area (response times below a second). STM studies of the (nonequilibrium) dynamics of electrodeposition/-dissolution with high temporal and spatial resolution can be performed using similar approaches as those described in the previous chapter for studies of surface transport in the double-layer regime. Using Video-STM fundamental atomic-scale processes during metal dissolution and (re)deposition can be directly observed, as illustrated in Fig. 16 for Cu(100) in HCl solution [7, 101, 102]. In this system removal and attachment of Cu along monoatomically high steps occurs strongly anisotropically (e.g., in Fig. 16 only along the step direction denoted as [010]), which was attributed

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Fig. 16 Series of successive in situ Video-STM images showing (a) local dissolution and (b) local growth of a terrace on Cu(100) in 0.01 M HCl solution. In both cases a strongly anisotropic process is found, caused by the presence of the c(2 × 2) Cl adlayer (5 × 8 nm2 , 10 frames/s video. Reprinted from ref. [7]. Copyright by Elsevier)

to the influence on co-adsorbed Cl anions. Specifically, according to these studies, the active sites of the deposition or dissolution reaction, kinks in the Cu steps (Fig. 16b, arrow), are determined by the ordered c(2 × 2) Cl adlattice, which exhibits a very different coordination at Cu steps running at 90◦ angles, resulting in a different reactivity of kinks in these steps. This is supported by Video-STM observations of isotropic growth and dissolution at the Cu(100) bilayer steps, which do not exhibit this adsorbate-induced structural anisotropy. Quantitative measurements of the kink propagation during Cu(100) dissolution in HCl solution, which allowed conclusions on the local reaction rates, were performed using a variation of the x–t scans described in Section 2.3 [103]. Although only line scan rates of 20 s−1 were used, kink propagation rates of the order of 103 s−1 could be measured by this technique. Even higher time resolution could, in principle, be obtained by combining this method with Video-STM scan rates. Despite these attempts, detailed quantitative studies of the nonequilibrium atomic-scale dynamics of dissolution and growth processes as have been performed for surfaces under equilibrium conditions are still largely lacking.

2.5 Scanning Tunneling Spectroscopy Beyond microscopic images, STM techniques can also provide local spectroscopic data, including data on electronic or vibronic excitations of single molecules and

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nanostructures. This feature is extensively used in nanoscience and has produced many spectacular results. Scanning tunneling spectroscopy (STS) is based on the dependence of the tunnel rate on the electronic structure of tip and sample and the distance-dependent tunnel probability (see refs. [1–4] for a detailed description). Typically, the tunnel current It is measured as a function of the tunnel bias Ubias or tip-sample distance ⌬z by sweeping Ubias or ⌬z over a wider range at a fixed sample position (or in some more elaborate experiments at every point of an STM image). Alternatively, the slopes dIt /dUbias or dIt /d⌬z are acquired parallel to the surface topography, which is a simple method to detect spatial variations in the spectroscopic signal. Since the signal also depends on the electronic structure of the tip, well-defined, stable tip states are an important requirement for STS measurements. The best data are obtained in UHV at cryogenic temperatures using tips that are prepared by well-defined methods and characterized by known spectroscopic features (e.g., surface states) of clean samples. At room temperature, especially in electrochemical environment, the tip stability is considerably reduced and more difficult to characterize. Under these conditions, the most reproducible data are obtained by “blunt” tips, which average the STM signal over larger surface areas, while tips capable of resolving atomic-scale features are usually less suited. Furthermore, at room temperature, spectroscopic features are thermally broadened, and thermal drift motion makes maintaining a constant position on top of a surface feature of interest difficult. Despite these problems, STS is gaining increasing attention for studies of electrochemical interfaces. The first in situ spectroscopic data in electrochemical environment were measurements of the tunnel barrier, that is, of the decay of It with increasing tip-sample distance. Early studies by several groups [104–106] revealed effective barrier heights ¯ of 1–2 eV, which is noticeable smaller than typical tunnel barriers obtained under ⌽ UHV conditions. The origin of this decrease in barrier height in the presence of the electrolyte solution, specifically of liquid water, was addressed in several theoretical studies, where it was attributed to the lowering of the metal work functions due to the electronic polarizability of the solvent [107] or to resonant tunneling via intermediate states formed by solvent fluctuations [108]. More recent models have taken the molecular structure of the solvent explicitly into account [109–113]. The most extensive of these calculations indicate that both effects indeed play a role [112, 113]. However, the resonant states in the solvent are found several eV above the Fermi level, that is, they act as virtual intermediate states. In the energy range where true resonant tunneling via water states would occur strong electron scattering, resulting in a loss of spatial resolution, was predicted. More detailed barrier height measurements by Vaught et al. indicated significant deviations from a true exponential decay at gap resistances below 108 ⍀, which were attributed to changes of the water structure in the thin tunnel gap [114]. More recently, Hugelmann and Schindler reported measurements of It (⌬z) over 6 orders of magnitude that exhib¯ with a period of 3.5 A ˚ (Fig. 17) ited clear (potential-independent) oscillations of ⌽ [115]. The latter were associated with the formation of discrete water layers in the tunnel gap. Similar phenomena were also observed in in situ STS studies on semiconductor samples [116]. Furthermore, very recent STS studies in pure water and

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Fig. 17 Local barrier height of the tunneling contact between a Au tip and a Au(111) sample in ¯ as a function of tip-sample dis0.02 M HClO4 , showing oscillations in the local barrier height ⌽ tance. At distances >0.9 nm reliable measurement of It is prevented by the increasing contribution of faradayic tip currents (Reprinted from ref. [115] with permission by the author. Copyright by Elsevier)

1 mM HClO4 where It and dIt /d⌬z were simultaneously acquired, even report a drop of dIt /d⌬z to zero below a critical distance, which was attributed to field-induced freezing of water in the tunnel gap at room temperature [117]. A general problem in all of these studies is to determine the absolute tip-sample distance. Usually, the position where the abrupt formation of a metal nanowire contact occurs (resulting in a jump in It ) is chosen as ⌬z = 0. However, according to a recent theoretical study, this assumption may result in an underestimation of the actual gap width by as much ˚ [35]. Nevertheless, studies of this type are not only important for a fundamenas 3 A tal understanding of in situ STM operation in electrochemical environment, but also may shed light on the electrolyte structure near the interface, a problem of considerable importance in interfacial electrochemistry. Applying the more powerful I/U tunneling spectroscopy to in situ studies of electrochemical interfaces is considerably more difficult, not only due to problems with tip stability and reproducibility (see above), but also due to the limited potential range. The available range of Ubias is at most ≈1 V in aqueous electrolytes, which is too small for most systems to show clear spectroscopic signatures, for example, of molecular adsorbates. Wider ranges of up to 4 V can be obtained in nonaqueous electrolytes and have been employed in in situ STS measurements to demonstrate semiconducting behavior of electrodeposited Ge films in ionic liquids [96]. However, as discussed above, the technical difficulties of studies in such electrolytes are substantial. In addition, very well isolated tips are required to keep the faradayic and capacitive currents at the tip significantly lower than It during sweeps of Ubias . For these experimental reasons in situ I/U spectroscopy has not gained wide usage till date. A variation of tunneling spectroscopy that is specific to the electrochemical environment has been first proposed on theoretical grounds by Schmickler and co-workers [118] and later demonstrated experimentally by Tao [119]. It is based

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a

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Fig. 18 (a) Schematic illustration of resonant tunneling via molecular states near the Fermi level of an adsorbed, redox-active molecule. (b) In situ STM images of a redox-active Fe(III) protoporphyrin and surrounding redox-inactive protoporphyrins on graphite at sample potentials Us of −0.15 (A), −0.42 (B), and −0.65 VSCE (top) and apparent height of the Fe(III) protoporphyrin as a function of Us , showing the increase close to the redox potential (Reprinted from ref. [119] with permission by the author. Copyright (1996) by American Physical Society)

on resonant tunneling via molecular states near the Fermi level of an adsorbed redox-active molecule, resulting in an increase in It (see Fig. 18a). A prerequisite for a significant effect is a fast and reversible electron transfer, which typically occurs if the reduced and oxidized molecular forms are similar and not strongly coupled to solvent modes. By changing the sample potential Us at constant Ubias the molecular states are shifted relative to the tunnel gap, leading to a resonant contribution if empty states of the molecules are situated in the energy window defined by Ubias . This configuration may be considered as a molecular field effect transistor with the electrolyte acting as the gate (i.e., Us acts as a gate voltage). First direct observations of this effect were reported by Tao for mixed protoporphyrin adlayers on HOPG, where the redox-active Fe(III) protoporphyrins appeared ˚ higher relative to the surrounding (redox-inactive) in the STM images up to 2 A protoporphyrins for sample potentials close to the redox potential (Fig. 18b). For this system, the shift in the molecular energy levels seems to be approximately equal to the change in electrode potential, which can be rationalized by the low density of states in the graphite substrate [120]. More recently, this spectroscopic approach has been applied to other systems such as metal nanoclusters attached to electrode surfaces via redox-active molecules [121] and molecular junctions, where the molecule is covalently bound to both sample and tip [122]. The possibility to modify the electron-transport properties of such nanoscale assemblies by employing the potential as a gate is a unique advantage of the electrochemical environment. In situ STS studies of this type are currently gaining increasing interest.

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3 Electrochemical AFM 3.1 Experimental Realization and Operation Modes In scanning force microscopy (also called atomic force microscopy, AFM) the force between the tip of the probe and the sample surface, which typically is in the range 10−12 –10−9 N, is used to control the tip-sample distance. Since its invention in 1986 [123] AFM has become the most popular scanning probe method. This is related to (a) its applicability to a wide variety of samples, including insulators and biological materials, (b) the large number of different force interactions (e.g., hard–core repulsive, attractive van der Waals, electrostatic, magnetic) that can be employed, (c) the possibility to easily measure local surface properties (e.g., adhesion, stiffness, and friction) in parallel to the surface topography, (d) the possibility to combine the force measurements with other local probe measurements, such as conductivity measurements using conducting tips or near-field spectroscopy studies (see Section 4), and (e) the more robust and user-friendly operation (as compared to STM) for studies on lateral length scales of micrometers. In the following chapter, the focus will be on the AFM operation modes commonly used in electrochemical environment. A more detailed, general description of AFM can be found elsewhere [2, 4]. For a basic understanding of scanning force microscopy first the different contributions to the force between an uncharged tip and a sample separated by a homogeneous medium (e.g., vacuum or a simple dielectric liquid) have to be considered in more detail (Fig. 19). The force between the outmost atoms of tip and sample (Fig. 19a and b, dotted lines) consists of the short-range repulsive interaction between the ion cores and the long-range attractive van der Waals interactions. However, the latter also are nonnegligible for atoms in the bulk of tip and sample separated by a larger distance. The sum of these long-range attractive forces (Fig. 19, dashed lines) usually is considerably larger than the local forces between the outmost atoms, which has important implications for the operation modes and the resulting lateral resolution of the AFM. For example, at small distances z the local repulsive forces may be largely compensated by the long-range attraction between tip and sample, that is, strong local forces may act on the tip atoms although

Fig. 19 Schematic illustration of (a) the tip-sample contact in an AFM and (b) the corresponding force distance curve F(z), showing short-range (dotted lines), long-range (dashed lines), and total forces (solid line) acting between the AFM tip and the sample

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the total, externally measurable force (Fig. 19b, solid line) is only weakly repulsive or even attractive. However, the long-range van der Waals interactions can be substantially reduced in water, which allows AFM operation at forces down to 10−11 N [124]. To measure the force the AFM tip is attached to a micromechanical cantilever, whose mechanical response provides the signal. Upon approach of the tip to the sample the attractive forces result in a small downward deflection of the cantilever until the force gradient exceeds the force constant of the cantilever and the tip snaps toward the surface (“jump-to-contact”). Further approach results in a continuous opposite deflection of the cantilever with a slope that depends on the stiffness of the sample. For stable feedback the AFM has to be operated in a part of the force-distance curve where the signal depends monotonically on z. In the simplest mode of operation, “contact-mode” AFM, the measurements are performed in the range of the repulsive interactions, where the force gradient is large, and the static deflection of the cantilever is used to determine the force. Since the local forces are large in this regime, contact-mode studies are restricted to sufficiently hard samples that are not mechanically modified during imaging. This problem is less severe in in situ AFM studies due to the screening of the van der Waals forces by the electrolyte solution (see above). The electrochemical environment therefore allows in general a gentler contact-mode imaging of surfaces than AFM studies in air or vacuum. In addition, contact-mode AFM allows to measure in parallel the friction force acting on the moving tip by monitoring the torsion of the cantilever. Studies of softer, mechanically less-stable surfaces require measurements in the attractive branch of the F(z) curve via a dynamic AFM mode, where mechanical oscillations of the cantilever along the z direction are induced. Typically, the cantilever is driven at a constant frequency close to the resonance frequency. The interaction of the tip with the surface causes a change in the resonance frequency, resulting in turn in a change in the oscillation amplitude, which provides the feedback signal. If the tip remains in the range of the attractive interactions over the entire oscillation period (“noncontact mode”) the influence of the tip on the surface is very small, however, also due to the long-range nature of the interactions the resolution is rather low. For this reason, an intermittent mode (“tapping-mode”) is used more frequently, where the tip is in brief contact with the surface at the outmost point of the oscillation. This results in a substantial increase in resolution as compared to noncontact mode, without exerting much larger lateral forces on the surface. Even higher resolution can be achieved using frequency-modulated AFM where the cantilever oscillates at a fixed, small amplitude and frequency is used as the signal [125–127] (see also Section 3.2). Almost all scanning force microscopes for operation in liquid environment are based on the same experimental setup, where the cantilever deflection is measured via the deflection of a laser beam, reflected from the back of the cantilever. The cantilever oscillation in dynamic AFM modes is generated either indirectly by inducing acoustic waves in the liquid via a piezoelectric actuator in the cantilever holder or directly by employing cantilevers with a magnetic coating on the backside that are

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excited electromagnetically. The latter in general allows more easy identification of the true cantilever resonance frequency, but the magnetic coating may be incompatible with the electrochemical environment. Both drive methods seem to afford a similar cantilever excitation and microscopic resolution [128]. AFM usually does not require electric measurements (apart from specialized experiments with conducting tips) and hence is easy to combine with potentiostatic or galvanostatic electrochemical control of the sample. Furthermore, commercially available AFM cantilevers (typically made from silicon or silicon nitride) feature tips that are (on scales of ≥10 nm) much better structurally defined than typical STM tips. Together with the ability of AFM to provide stable images on nonconductive (e.g., passivated) surface areas, these properties make AFM often superior to STM in studies of technical electrode surfaces and applied electrochemical processes. Earlier reviews of AFM in electrochemical environment can be found in ref. [14, 18].

3.2 In Situ AFM Imaging of Electrode Surfaces Since the samples in electrochemical systems usually are electronically conducting, the key advantage of AFM over STM, that is, the possibility to study isolator surfaces, is of lesser importance. For this reason STM, which in general provides higher microscopic resolution, is still more frequently employed than AFM for in situ studies of electrochemical systems. Nevertheless, in situ AFM has been widely used for the microscopic characterization of electrode surfaces, ranging from atomicresolution images to studies of the surface morphology on the ␮m scale. The possibility to resolve the atomic lattice of bare metal electrode surfaces and metal adlayers was demonstrated by Mane et al. in a study of Cu UPD on Au(111) by contact-mode AFM [129]. Since then, a large number of atomic resolution in situ AFM studies have been reported, including studies of various metal and salt-like adlayers, oxide films, and organic adsorbates (see ref. [14] for an overview). As an example, contact-mode AFM observations of Bi UPD on Au(111) are shown in Fig. 20, illustrating resolution of the Au substrate lattice (Fig. 20a), as well as of a (2 × 2) (Fig. 20b) and an uniaxially incommensurate (Fig. 20c) Bi-adlayer [130], in good agreement with a complementary surface X-ray diffraction study [131]. Although such high-resolution contact-mode AFM images can clearly resolve the surface lattice structure, the forces are typically so large that a wider area of the tip is in contact with the surface rather than only the apex atom of the AFM tip. Atomic resolution can in this case result if the atomic lattice at the tip locks into the sample lattice during scanning, leading to a corrugation with the periodicity of the lattice spacing. Experimental evidence for this is the characteristic absence of deviations from a periodic lattice, that is, of surface defects, such as vacancies, domain boundaries, or substrate steps, in the AFM images. Since AFM and STM employ different interactions, comparative studies by both techniques may give complementary data, which may help to clarify the surface structure. As shown in Fig. 21 for a guanine monolayer on graphite electrodes, the

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Fig. 20 In situ contact-mode AFM images of Au(111) in 0.1 M HClO4 solution (a) positive of the Bi UPD range, showing the Au substrate lattice, (b) in the range of the (2 × 2) Bi UPD adlayer phase, and (c) in the range of the uniaxially incommensurate Bi UPD adlayer phase (5 × 5 nm2 . Reprinted from ref. [130] with permission by the author. Copyright by American Chemical Society)

Fig. 21 (a) In situ contact-mode AFM and (b) in situ STM images of a guanine monolayer on graphite in 0.1 M NaCl solution (5 × 5 nm2 . Reprinted from ref. [132] with permission by the author. Copyright by American Chemical Society)

in situ AFM (Fig. 21a) and STM (Fig. 21b) images both resolve a molecular structure with identical lattice parameters, but clearly differ with respect to details of the image within the unit cell [132]. In principle, noncontact AFM probes the ion cores (i.e., the total electron density) and AFM images consequently should reflect more closely the geometric surface structure than STM images, which are (within the Tersoff–Haman approximation) determined primarily by the electron density at the Fermi level (see Section 2.2). However, the influence of the tip structure on both STM and AFM images makes a detailed analysis of the differences in the images difficult if not outright impossible. This problem may be overcome by frequencymodulated AFM, where the interaction between the outmost tip and the surface is dominant. This technique has been recently shown to be capable of true atomicresolution imaging with an image quality equal or even surpassing high-resolution STM [126, 127]. Up to now frequency-modulated AFM has been performed almost

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exclusively under UHV conditions. Very recently, the adaptation of this method to measurements in liquid environment has been demonstrated [133, 134], suggesting that frequency-modulated AFM may develop into a promising future method for electrochemical surface science. Similar to scanning tunneling microscopy, scanning force microscopy has been extensively used for microscopic studies of a wide range of electrode processes, for example, electrodeposition or dissolution processes. Compared to STM, local surface features such as steps are less well resolved by AFM. On the other hand, the AFM tip is usually more stable and the imaging is less affected by changing electrochemical conditions. For these reasons, AFM is generally preferred for studies on the mesoscopic scale (i.e., for scan ranges from 0.5 to 100 ␮m). In particular, AFM is superior to STM for studies on strongly heterogeneous samples, where materials with different electronic properties (e.g., oxides and metals) coexist in the studied surface area. For example, AFM has been successfully employed to study the electrodeposition of Pb [135] and Au [136] on Si(111) electrode surfaces, whereas stable STM imaging proved difficult due to the strongly different imaging conditions required for the metal and the semiconductor surface. Another import field is corrosion, where the samples are often covered by oxide films with poor electronic conductivity and where AFM is the method of choice, particularly in applied corrosion studies (see also Chapter 10). Apart from qualitative observations of the surface morphology larger-scale AFM images can also be analyzed quantitatively. Specifically, systematic quantitative studies of the surface roughness can provide insights into the mechanisms of growth and dissolution processes. An elegant example is the evaluation of the morphology of electrodeposited Cu films (Fig. 22a) by scaling analysis, performed by Hou and Schwarzacher [137]. In this type of studies, the dependence of the root-mean-square surface width w(l) on the lateral length scale l over which w(l) is measured and on the deposition time is analyzed (Fig. 22b). For deposition from pure, additive-free sulfate electrolyte, the surface roughness could only at low current density (4 mA cm−2 at 0.3 M Cu2+ concentration) be described

a

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Fig. 22 AFM studies of the morphology of Cu deposits formed by electrodeposition from acidic 0.3 M CuSO4 solution. (a) AFM image for 1 min deposition time. (b) Scaling analysis, showing the surface width w(l) over regions of length l for different deposition times (Reprinted from ref. [137] with permission by the author. Copyright (2001) by American Physical Society)

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by normal dynamic scaling, where w is independent of deposition time at low l. In contrast, at higher current density (≥16 mA cm−2 ) anomalous scaling was observed, where an extra scaling exponent β loc is required to describe the time evolution of the roughness at short-length scales (β loc = 0.30 for the data shown in Fig. 22b). The origin of this behavior, although not yet completely understood, may be related to surface transport during deposition. Studies of this type may help to unravel the complex mechanisms of polycrystalline film growth. In situ dynamic AFM in liquid environment is primarily used to study soft samples, for example, biological systems or polymers, where it has become a major technique for high-resolution imaging and characterization of local material properties. While numerous dynamic AFM studies on nonconducting substrates (e.g., mica) exist, only a few in situ studies of electrochemical systems have been reported, primarily in the field of bioelectrochemistry. An early example was a tappingmode AFM study by Boussaad and Tao of myoglobin on bare graphite electrodes and graphite modified by a didodecyldimethylammonium bromide self-assembled monolayer [138], an important model system for studying electron transfer reactions in proteins. More recently, it has been shown that dynamic AFM can be combined with scanning electrochemical microscopy (see Section 4) to study in parallel the structure and electrochemical reactivity of soft biological samples [139]. Although the preparation of the conducting, partly isolated AFM tips required for these measurements is substantial, modern microstructuring methods may help to build suitable probes on a routine base [139, 140]. Such combined SPM studies could develop into a valuable tool to unravel complex bioprocesses on the nanometer scale.

3.3 Forces at Electrochemical Interfaces The quantitative determination of forces at interfaces is another important area of application for AFM. Often specialized instruments with improved force detection and very linear tip movement along the surface normal direction are employed in these experiments. For precise force measurements, probes with cantilevers of known spring constant and defined tip geometry are required. The latter is usually difficult with common microfabricated silicon or silicon nitride tips, which provide high lateral resolution, but usually have an ill-defined apex geometry. In an alternative approach, special probes have been employed, where the tip consists of a spherical microparticle (typically silica spheres of 2–20 ␮m diameter), glued to the cantilever. The low surface roughness and well-defined curvature of these probes, leading to a similar configuration as in the older surface-force apparatus, allows to quantitatively determine the interactions with the sample and to compare those experimental results with quantitative theories. The forces between two solids immersed in electrolyte solutions contain contributions from van der Waals forces and electrostatic double-layer forces, resulting from the mutual perturbations of the double layers at both solid surfaces at small separations. Most of these experiments were performed on insulators, where the

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surface charge is mainly determined by the pH. Some of the first AFM studies of metal electrodes used Au electrodes and silicon nitride tips [141] or silica spheres [142] as probes. As expected, the force on the negatively charged probes depended on the surface charge of the Au electrode: while repulsive interactions were found in the potential regime of the negatively charged surface (i.e., at potentials below the potential of zero charge), the probe is attracted to the surface at positive surface charges. Furthermore, the force curves were in good agreement with predictions from Derjaguin–Landau–Verwey–Overbeek (DLVO) theory at large separations. A detailed treatment of the investigation of double-layer forces by AFM and its theoretical basis is beyond the scope of this chapter, but can be found elsewhere [16, 143]. In addition, AFM-based force measurements can be used to probe more shortrange, chemical interactions, including adhesive forces and elastic properties of adsorbed molecules. Spectacular examples of this are force spectroscopy studies of single molecules that allowed to directly obtain mechanical molecular properties [144–147]. Studies at electrochemical interfaces have not yet reached the single molecule level. However, studies of the adhesion forces between tips and metal electrodes functionalized by organic molecules become increasingly popular and permitted to measure quantitatively properties, such as surface and interface free energy [148, 149]. An overview of the earlier work in this rapidly growing field can be found in ref. [150].

4 Other SPM Techniques Apart from STM and AFM scanning electrochemical microscopy (SECM) and scanning near-field optical microscopy (SNOM) are of relevance to electrochemical nanoscience. SECM is a genuine electrochemical SPM technique, where the sample is scanned by an ultramicroelectrode (UME), whose current or potential provides the signal (see also Chapter 11) [17, 151–154]. A common mode of operation is the feedback mode, where a redox-active mediator species is consumed at the UME. If the mediator is regenerated at the sample the probe current increases with decreasing probe-sample distance (“positive feedback”), otherwise it decreases (“negative feedback”). Although the spatial resolution of SECM is usually only in the micrometer range, it provides a valuable technique for measuring local (electro) chemical reactivity. Furthermore, SECM-based approaches can also be used to modify surfaces locally via electrochemical reactions (e.g., deposition, etching, and oxidation) at the probe position, enabling the formation of micro- and nanoscale structures (see Section 5). SECM has been successfully combined with STM as well as contact and noncontact AFM, allowing parallel characterization of surface structure and electrochemical properties [27, 139, 140, 155] (see also Section 3.2). Although SNOM has not been used extensively till date in electrochemical environment, it offers good prospects for future in situ studies. SNOM allows optical near-field studies with lateral resolution far below the wavelength of the employed

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light [2]. It employs local electromagnetic fields generated either via submicrometer apertures or metal tips. The latter “apertureless SNOM” is based on the huge enhancement of optical fields in nanoscale gaps. A particularly exciting new development is tip-enhanced Raman or infrared spectroscopy, which offers prospects to combine the high spatial resolution of SPM methods with the chemical sensitivity of vibrational spectroscopy. Recent experiments indicate that optical signals from areas of less than 10 nm extension can be obtained, enabling studies of small ensembles of molecular adsorbates and individual nanoparticles [156, 157].

5 Nanostructuring by Electrochemical SPM 5.1 Nanostructuring by Local Mechanical Interactions SPMs can not only be employed for imaging, but also for controlled modification of surfaces on the nanoscale (see, e.g., ref. [158, 159] for a detailed overview). The most spectacular example of this is the positioning of individual atoms on surfaces by low-temperature UHV-STM [160], which opens up opportunities to directly study quantum physical phenomena (e.g., standing electron waves in quantum corrals [5, 161, 162]) or chemical processes (e.g., tip-induced catalytical reactions [163]). For practical purposes larger-scale structures with dimensions of a few nanometers, which are stable at room temperature, are of considerable interest, for example, for catalysis or nanoscale electronics. SPM-based nanostructuring methods also allow the preparation of this type of structures. In the simplest of approaches, this is done by mechanical contact between tip and sample, leading to a mechanical deformation of the surface or to the transfer of material between tip and sample, as has been demonstrated already in early STM studies by Gimzewski et al. [164]. SPM in electrochemical environment allows to develop the latter type of methods into more sophisticated techniques, where local mechanical modification by the tip is combined with an electrochemical process, in general, electrodeposition or dissolution. Typically, the mechanical interaction in these approaches defines the nanostructure dimension, whereas the electrochemical process provides the material for the formation of the structure. A very simple method is to use the tip as a nanomechanical tool for the creation of defects in the sample surface, which subsequently act as a preferred nucleation sites, resulting in local electrochemical deposition or dissolution at this site. One of the earliest examples of this method was reported by the group of Penner for STM-induced nucleation of metal electrodeposition on graphite [158, 165, 166]. In this study, a defect in the graphite surface was generated by applying a voltage pulse to the STM tip, which subsequently could be decorated selectively by electrodeposition. Obviously, this technique works best if the overpotential for nucleation on the original sample is much higher than that for nucleation at the induced defect. The latter can be easily achieved on samples covered by a passivating layer, which is locally removed by the tip (Fig. 23a). Examples

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a

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Fig. 23 (a) Schematic illustration of nanostructuring by electrochemical decoration of SPMinduced defects. (b) Cu lines formed by Cu electrodeposition on AFM-scratched p-type Si(100) (Reprinted from ref. [168] with permission by the author. Copyright 2001 by American Institute of Physics)

of this approach include submicron structures formed by local electrodeposition of Cu on AFM-induced defects in oxidized Cu surfaces [167] or of Cu and Pd onto AFM-scratched silicon surfaces [168, 169] (Fig. 23b). An alternative method, where material is first electrodeposited on an STM tip and then mechanically transferred to the surface (Fig. 24a), was developed and extensively employed by Kolb and co-workers [170–174]. In this method, the tip potential is kept slightly negative of the Nernst potential, resulting in continuous metal loading of the tip, whereas the sample potential is kept ≈10 mV positive of the Nernst potential to avoid bulk deposition. The mass transfer from the tip to the sample is initiated by approaching the sample close enough that a metal bridge between tip and sample is formed (“jump to contact”; Fig. 24a, right). This bridge breaks during subsequent retraction of the tip, leaving a small metal cluster on the sample surface (Fig. 24b). The cluster height of 1–4 monolayers can be controlled by the tip displacement Δz during approach. For fast electrodeposition processes (e.g., of Cu) cluster formation at kHz rates has been demonstrated, allowing preparation of large, highly uniform cluster arrays in a few minutes. Transfer of material from the tip to the sample can only occur if the adhesion of the deposit to the sample metal exceeds

a

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Fig. 24 (a) Schematic illustration of nanostructuring via electrodeposition on the tip and subsequent mechanical transfer to the sample. (b) Five rows of five Cu clusters each formed on Au(111) by this method. The tip displacement Δz increases from right to left, resulting in an increased cluster size (Reprinted from ref. [172] with permission by the author. Copyright by Elsevier)

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the cohesion within the deposit, that is, in systems where underpotential deposition of the admetal is observed and the sample is consequently covered by a UPD adlayer. This is confirmed by the experimental observation that well-defined clusters can only be generated in UPD systems (e.g., Cu [170–172] or Pd [173, 175] on Au(111)), whereas in non-UPD systems cluster formation does not (e.g., for Ni on Au(111) [174]) or only erratically (e.g., for Cu on Ag(111) [172]) occur. In addition, computer simulations of this nanostructuring process indicated substantial alloying with the substrate during cluster formation, which may explain the exceptionally high stability of these clusters against electrochemical dissolution [175, 176]. However, this point is still under debate [174]. Overall, this tip-induced cluster formation is, till date, in terms of reproducibility and achievable feature size, one of the most successful examples of nanostructure formation by in situ SPM and has, despite its limitation to certain material combinations, greatly stimulated interest in electrochemical nanostructuring methods.

5.2 Nanostructuring by Modification of the Local Electrochemistry Rather than using the tip of an in situ SPM as a nanomechanical tool, it also can be employed to change the electrochemical conditions at the interface. In the simplest case, the composition of the solution is locally changed by an electrochemical process at the tip, which is kept a few nanometers away from the surface. This composition change triggers a change in the local rates of an electrochemical reaction at the sample surface in the vicinity of the tip position. Conceptually, this approach is identical to operating the SPM in an SECM mode, differing mainly in the tip geometry: SPM tips are usually much sharper than SECM tips, but feature less well-defined tip geometry, making a quantitative description of the involved electrochemical and transport processes difficult. The formation of metal nanostructures on metal and semiconductor electrodes by this method was reported by Lorenz, Schindler, and co-workers [177–179]. In these studies, the STM was operated in a metal ion-containing electrolyte with the sample potential being kept slightly more positive than the nucleation threshold (Fig. 25a). The nanostructure was formed by first loading the tip with a metal by electrodeposition from solution, followed by stepping the tip potential to a very positive value, resulting in rapid redissolution of the deposit. Due to the resulting supersaturation electrochemical nucleation and growth of a metal cluster with typical diameters of 10–30 nm occurs. Examples of nanoclusters prepared by this technique include Co clusters on Au(111) and Pb on Si(111) (Fig. 25b) [177–179]. Local changes in the electrochemical behavior of the sample can also be induced by directly influencing the electrochemical reactions at the underlying electrode surface by the tip. Since the tip-sample distance in SPM is very small (e.g., typically ≈1 nm in STM), the electrochemical double layers of tip and sample can overlap, which may affect the electrostatic conditions, the electron transfer, and the mass transport in the gap between tip and sample. For example, locally enhanced

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Fig. 25 (a) Schematic illustration of SPM-based nanostructuring, based on changing the local electrolyte composition via burst-like dissolution of previously electrodeposited material from the tip. (b) Two 22-nm diameter Pb clusters on n-type Si(111), prepared subsequently by local electrolyte supersaturation via Pb desorption from the STM tip (Reprinted from ref. [179] with permission by the author. Copyright by Elsevier)

metal dissolution rates of Cu [180] and Ag [181] electrodes at the tip position were observed in in situ STM studies if the tip potential was kept positive of the sample potential (i.e., at negative Ubias ). This phenomenon was tentatively attributed to an oxidation of metal surface atoms induced by the tunneling of electrons from the sample to the tip [180]. Due to the high local-current density at the tip position such a process may cause a noticeably increased dissolution rate even if its efficiency is very low. Schuster et al. introduced an interesting technique, where nanosecond pulses are employed to spatially confine electrochemical reactions, allowing the electrochemical machining of the sample with submicrometer precision [182, 183]. The characteristic timescale for double-layer charging, required for establishing the potential on the solution side of the interface, depends on the electrolyte resistance between tip and sample, which is orders of magnitudes smaller at sample areas close to the tip position (see Fig. 26a). By applying suitable chosen nanosecond pulses to the tip (or an arbitrary-shaped metal tool) a deposition or dissolution reaction may be limited to areas within submicrometer distances of the tip. As illustrated by the 5-␮m deep spiral trough shown in Fig. 26b features with dimensions approaching 100 nm and a surface roughness of a few 10 nm can be etched by this method. Furthermore, not only etching of various metals and silicon surfaces, but also local electrodeposition has been demonstrated [182], making this technique a versatile tool for electrochemical micro- and possibly also nanostructuring.

5.3 Nanostructuring by Electrochemical Nanocells An alternative to performing the nanostructuring in a bulk electrolyte is to confine the electrochemical environment to a droplet of nanometer dimensions (i.e., an electrochemical “nanocell”) between tip apex and sample (Fig. 27a). The most popular

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a

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Fig. 26 (a) Principle of electrochemical micromachining by locally confined double-layer charging via ns-pulses, illustrating schematically the differences in the electrolyte resistance at different sample locations. (b) Spiral trough etched into Ni sheet using 3 ns pulses of 2 V (Reprinted from ref. [183] with permission by the author. Copyright by Elsevier)

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e–

Fig. 27 (a) Schematic illustration of SPM-based nanostructuring methods, utilizing the tip-sample gap as an electrochemical nano cell. (b) Multiple mercaptopropyltrimethoxysilane lines prepared by dip-pen nanolithography combined with electro-oxidation via the AFM tip (Reprinted from ref. [191] with permission by the author. Copyright by American Chemical Society)

method based on this principle is a local oxidation of the sample by a conducting AFM tip. Although a number of metals and semiconductors that form stable oxides have been similarly nanostructured, most studies have focused on the local oxidation of Al and Si. The lateral dimensions and oxide thickness can be controlled by the ambient humidity, the applied voltage, and the tip-scanning speed. In addition, apart from test structures, simple devices, such as a single-electron transistor [184], have been fabricated. An overview of the extensive work done in this area is given in ref. [159, 185]. An interesting variation of the “nanocell” method was reported by Maoz et al., who employed it to electrochemical-pattern organic monolayers by tip-induced oxidation or reduction [186, 187]. Local electrochemistry in the liquid meniscus between tip and sample can also be combined with “dip-pen” nanolithography, where molecules are applied to the tip and then transferred via capillary transport through the meniscus onto the

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sample [188]. Liu and co-workers have introduced an electrochemical “dip-pen” method that utilizes local electrochemical reduction or oxidation reactions involving the delivered molecules, which allowed direct writing of metal or oxide lines and selective local etching of the surface [189, 190]. Cai and Ocko have combined “dip-pen” nanolithography with the approach of Maoz et al. demonstrating local conversion of an organic monolayer into a reactive state and “dip-pen” delivery of molecules (e.g., silanes) binding to these activated surface areas in a single sweep of the AFM tip [191]. As shown in Fig. 27b (right graph), subsequent application of this method even allows the formation of defined multilayer structures built by these molecules. Altogether, SPM nanostructuring methods employing an electrochemical nanocell are among the most versatile techniques to create structural or chemical pattern on surface with dimensions from a few 10 nm to the ␮m range and consequently have become very popular in the last years.

6 Conclusions SPMs, in particular, scanning tunneling and scanning force microscopy, had and still have a significant part in ushering in a paradigm change toward true science and technology on the nanoscale. The possibility to view, analyze, and to manipulate surfaces down to atomic dimensions afforded by these methods makes them indispensable tools in a wide variety of fields, including electrochemistry. Because only few techniques allow in situ structure-sensitive studies of electrochemical interfaces, SPM methods were strongly embraced and have significantly contributed to a true microscopic picture of electrode surfaces and electrochemical processes since their introduction at the end of the 1980s of the last century. To the achievements of in situ SPM techniques belongs the clarification of the adlayer structure in a large number of adsorbate systems, the study of the mechanisms of phase-formation processes, such as electrochemical metal deposition, dissolution, and oxidation, the investigation of mass transport at electrochemical surfaces, and the study of doublelayer structure and electron transfer by SPM spectroscopy. Furthermore, various nanostructuring methods which are based on the combination of SPM with electrochemical methods have been developed. Emerging trends are to apply SPM to even more complex systems and to employ it as a tool for the quantitative determination of local interface properties and elementary steps in electrochemical reactions. This will, in part, require multifunctional probes that allow to simultaneously measure different physical quantities or approaches that provide new information, for example, local chemical sensitivity. As has been discussed in this chapter, exciting new developments in this area are currently emerging.

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X-ray Lithography Techniques, LIGA-Based Microsystem Manufacturing: The Electrochemistry of Through-Mold Deposition and Material Properties James J. Kelly and S.H. Goods

1 Introduction to LIGA Fabrication and Its Applications Certain microsystem fabrication techniques are critically dependent on the electrochemistry of metal deposition into lithographically defined features that are developed in insulating molding materials. One such technique, developed originally at the Forschungzentrum Karlsruhe, Germany, is known as LIGA, the German acronym for lithography, electroplating, and replication (Lithographie, Galvanoformung, and Abformung) [1–3]. An example of typical miniature structures formed by plating through thick photoresist (the insulating molding materials) is shown in Fig. 1. Since its inception in Germany in the 1980s, LIGA research activities have expanded throughout Europe, as well as in Asia and North America. Thanks to the intense and collimated X-ray synchrotron radiation used in the lithography step, the definition of high aspect ratio features in thick photoresist with good-dimensional fidelity is a unique attribute of the technique [4]. For example, high aspect ratio features (i.e., the height-to-width ratio) as high as 100 and feature depths up to ≈1 mm have been realized. These features are then filled with a metal via electrodeposition through the X-ray exposed photoresist mold that is bonded to a conductive substrate (the details of the LIGA process and other LIGA-like processes will be discussed later in this chapter). The unique geometries encountered in LIGA through-mask electrodeposition present distinct challenges. This is particularly the case with respect to the resultant materials that are required to have special properties (e.g., mechanical performance characteristics or magnetic properties). Consequently, a substantial portion of LIGA research is dedicated to first understand the electrochemistry of the LIGA through-mask electrodeposition process, and second, the subsequent material properties for electrodeposited metals, alloys, and metal-matrix composites [5–6].

James J. Kelly (B) IBM, Electrochemical Processes, 255 Fuller Rd., Albany, NY 12203, USA e-mail: [email protected]

P. Schmuki, S. Virtanen (eds.), Electrochemistry at the Nanoscale, Nanostructure Science and Technology, DOI 10.1007/978-0-387-73582-5 3,  C Springer Science+Business Media, LLC 2009

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80 Fig. 1 Example of Ni structures fabricated by electroplating through PMMA resist that had been patterned by X-ray lithography. This technique of using electrodeposition to deposit metal into molds that have been lithographically formed with X-ray synchrotron radiation is referred to as the LIGA technique (German for lithographie, galvanoformung, and abformung; in English, lithography, electroplating, and replication). The top optical shows a variety of structures still attached to the metallized substrate. The lower image is an scanning electron micrograph showing a portion of a released structure. Images courtesy of Georg Aigeldinger, Sandia National Laboratories, Livermore, California

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1 mm

Most structures fabricated with the LIGA process generally have critical lithographic dimensions on the micron scale [2]. In principle, submicron features are possible, but such fine features are not routinely fabricated [2, 7]. Although the physical dimensions of LIGA-fabricated components are rarely on the nanoscale, important microstructural aspects of the electrodeposit often are. For example, electrodeposited materials are well known for exhibiting fine microstructures, with grain sizes in the nm range [8]. In fact, this is somewhat fortuitous, as a grain size on a scale much smaller than that of the physical component dimensions is usually a requisite for that component to have a spatially uniform microstructure. But, as will be discussed later, the degree of this uniformity usually depends on the presence of other species (other metal ions, additives, or adsorbed species, for example) that may affect the deposit structure, particularly when the concentration of these species is sensitive to transport. Our objective here is not a detailed review of the LIGA process or its technological applications; several reviews of this type are available [9–15]. Instead,

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focus is on the unique aspects of the electrochemistry of LIGA through-mask metal deposition and the generation of the fine and uniform microstructures necessary to ensure proper functionality of LIGA components. Before addressing these issues, brief descriptions of the LIGA process, its history, and applications are given for those unfamiliar with the technique.

1.1 LIGA Process Flow The general flow of the process steps necessary to create LIGA microparts is shown in Fig. 2. The process consists of using synchrotron X-rays and an X-ray absorbing mask to transfer a desired pattern to a metallized wafer substrate on to which is bonded a thick, X-ray photoresist blank. This photoresist is most commonly high molecular weight polymethylmethacrylate (PMMA) which is rendered more susceptible to chemical dissolution by X-ray exposure. The resist is then “developed” using a commercial solvent to create prismatic cavities into which metal is electrodeposited. The remaining PMMA is then dissolved, and the prismatic metallic structures can be released by chemically dissolving the original metallization layer. What we have described here and shown in Fig. 1 is, in fact, often referred to as “direct” LIGA, wherein the final released parts are those intended to be used. Often, perhaps more typically, the final part is a monolith consisting of the electrodeposited structures attached to a backing plate (either the plating substrate itself or a top surface blank formed by overplating the mold). This “parent” tool is then used to replicate multiple generations of microparts in a variety of ways.

Plating Base

Gold Mask Lithography

PMMA

Synchrotron x-rays

Development

Electrodeposition

Dissolution/Part release

Fig. 2 Schematic diagram of the LIGA process flow. A LIGA mold consisting of a plating base (usually a metallized wafer) with thick PMMA resist is patterned with synchrotron X-rays by using a gold X-ray-absorbing mask. The features are developed and then electroplated, after which dissolution of the PMMA may take place. In the case shown here, the parts are released from the plating base to yield separate piece parts

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Pattern Layout – Before starting the LIGA process shown in Fig. 2, a pattern layout must be created in order to fabricate the X-ray-absorbing mask that will be used during exposure. This entails taking a desired two-dimensional device geometry from a drawing (from CAD software, for example) and distributing it across an area corresponding to the surface of a wafer substrate. An example of a pattern layout of a spring prototype is shown in Fig. 3a. Unless special exposure techniques are employed [2], LIGA-fabricated devices are prismatic, that is, the part geometry does not vary in the z dimension, which is perpendicular to the substrate. Figure 3b shows the final-plated LIGA component from the layout shown in Fig. 3a. A fair amount of experience is involved in arranging the devices judiciously across the wafer so as to facilitate subsequent processing. For example, a certain minimum separation distance between features may be desired to avoid thin, fragile areas of resist. Also, since large regions of uninterrupted resist tend to lead to significant physical distortions due to swelling and thermal expansion, ancillary structures may be added to improve the dimensional fidelity of features in critical regions. Where dimensional tolerances are of particular concern, these ancillary structures

a)

b)

ca. 10 mm

Fig. 3 (a) A layout of spring prototypes used in the photolithography necessary to fabricate the gold X-ray absorbing mask. The colored areas correspond to regions where thin UV resist remains after patterning for the X-ray mask. Since thick gold (several to tens of microns) is electroplated around and through these thin resist features to form the X-ray-absorbing mask, the pattern is transferred into the PMMA resist as its negative (the lack of thick gold in this region allows Xrays to impinge on the PMMA, sensitizing it for development to form open features in the resist). These features are in turn filled with electroplated metal, producing a final part after mechanical planarization and release from the substrate as shown in (b). Layout image courtesy of M. Hekmati and L. Hunter of Sandia National Laboratories, Livermore CA

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are placed close to and conformal to part features. The intent is to minimize the uninterrupted length of resist immediately adjacent to these critically dimensioned structures, reducing the overall swelling and CTE-driven distortions. This also has the beneficial effect with respect to the electrodeposition process itself. By placing openings in large unpatterned areas of the resist, these ancillary features improve the homogeneity of the overall wafer with respect to the “active area density”[16], making the pattern-scale current distribution more uniform. This improves the overall uniformity with respect to deposition rate, which in turn, may favorably influence material properties and structure. In Fig. 3a, the moat-like features surrounding the spring geometry are an example of a structure serving these purposes, and as an added benefit, they can be used as sacrificial samples for materials analysis. One other benefit derived from these ancillary structures is the fact that they help support critical features during planarization and lapping, avoiding the tendency for fine features to lap faster (resulting in thinner in-plane dimensions) than neighboring large features. Once an acceptable layout of desired parts is obtained, one may proceed with the production of the X-ray-absorbing mask. Mask Substrate – The fabrication procedure for an X-ray mask mainly depends on the particular X-ray spectrum at the synchrotron facility. Thicker absorbers are typically needed when the X-ray energies used are relatively high, and the exact absorber thickness required for a given X-ray spectrum has been worked out by a number of groups [2, 17–18]. Electrodeposited gold is usually used as the absorbing material, although other materials and deposition processes have been investigated [2]. We limit our discussion to the more common method that involves the use of electroplated gold. For low absorber thicknesses (<10 ␮m), thin metallic membrane substrates can be used; this is usually the situation at synchrotron beamlines delivering a soft (low-energy) X-ray spectrum. At such soft sources, the substrate must be sufficiently “transparent” to X-rays to allow them to pass through the unmasked regions. Titanium has been used as an X-ray-transparent membrane for this purpose (as well as other materials) [2]. In this instance, after patterning and deposition of the absorber gold, the titanium is partially etched away from the area of interest (usually the center of a wafer) resulting in an X-ray-transparent membrane that is supported by thicker annular ring or “picture frame” of Ti. For harder X-ray sources, thicker absorbers (>10 ␮m) must be used, and the substrates are required to have greater mechanical integrity to support the patterned absorber gold. For this mask type, silicon and beryllium are often used as sheet substrates in thickness that can range from 100 to 500 ␮m. If the substrate is not conductive, a thin metallization layer is applied. Since the X-ray spectrum employed is fairly hard in this situation, X-ray transparency in the unmasked regions is generally of less concern. Mask Photoresist – The next step, the patterning of photoresist, is the same for either approach. Commercially available photoresist of a desired thickness is patterned by standard contact UV lithography to define the pattern-layout geometry on the mask. Where the gold is deposited (whether as the positive or negative of the feature to be fabricated) depends on the development characteristics of the mold

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photoresist used to pattern the structures to be electroformed. This is the so-called tone of the mask. Regardless, only the active (electrically conductive) areas receive the plated gold. The thickness of the resist must be about 25% higher than the target thickness of the deposited gold so as to not overplate the resist (which would reduce the dimensional fidelity of the final electrodeposited structures). Sulfite baths are often used for the gold deposition to avoid damaging the UV mask photoresist. After gold deposition, the resist is usually removed from the mask by dissolution in a solvent. Since high-precision patterning of UV photoresist becomes more difficult with increasing resist thickness [2], thin absorbers on membrane masks yield the greatest precision for small features. Sheet-substrate masks with thicker absorber gold may be mechanically more robust, but tend to be used for less demanding, more routine LIGA prototyping where high tolerances are less critical. These sheet-substrate masks are convenient as the entire wafer area is available for processing, whereas for membrane masks, only the thinned region may be used. Generally speaking, for mask resist measuring a few microns in thickness, features may be reliably defined down to about a micron in width, although process limits will vary with lithography infrastructure at a given laboratory [2]. More advanced techniques for defining finer features for submicron LIGA will be discussed at a later point [2, 7]. Mold Exposure – After an X-ray mask is in hand, the next step in the LIGA process is the exposure at a synchrotron to produce molds for the subsequent electrodeposition step. The molds, consisting of wafers bearing PMMA photoresist of a desired thickness, must be prepared in advance. This entails the bonding of a disk of PMMA to the wafer that has been metallized with a conductive seed layer for subsequent electrodeposition. The exposure of these molds necessitates a substantial level of infrastructure. At a minimum, an apparatus for holding and translating the mold so as to expose the entire wafer to the X-ray beam is required. More sophisticated equipment is necessary for more advanced exposure techniques, such as angled exposures to produce graded side walls, or alignment tools for multilevel processing that require multiple masks and X-ray exposures [2]. The mask is placed between the X-ray source and the mold, allowing the X-rays to pass through the areas where there is no gold absorber. The X-rays that pass through the mask impinge on the PMMA, scissioning the PMMA polymer chains, thereby sensitizing it to dissolution in the subsequent development step. The exposure times are dictated by the characteristics of the X-ray source, beamline parameters (mirrors and filters), mask substrate material and thickness, and finally, the thickness of the PMMA resist [17]. Mold Development and Seed Layer Preparation – After exposure, the X-rayexposed regions of the PMMA may be dissolved by immersion of the mold in an appropriate chemical developer. Developers are mixtures of various organic solvents formulated to selectively dissolve the exposed PMMA, while leaving behind undissolved, unexposed PMMA. In this way, the geometry of the discrete structures on the mold is defined. Dissolution times depend on the mold thickness and specific development conditions, but typically range from a few minutes to several hours.

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When development is complete (confirmation may necessitate observing features under a microscope to check for residual PMMA at the bottom of the exposed mold features), the mold is rinsed with deionized water and dried. Depending on the metallization applied to the wafer, certain dry or wet etching processes may be necessary after development to fully reveal the desired metal seed layer. A number of materials have been used as conductive seed surfaces in LIGA [19–20]. Since the X-rays may interact with the seed layer material during exposure, some consideration must be given to the choice of metal used. These interactions often involve the emission of secondary radiation that may damage (overexpose) the PMMA/wafer interface. These aspects will be discussed in more detail in the electrodeposition section. Electrodeposition – In order for the electrodeposition reaction to start, the seed surface must be first wetted by the electrolyte. This is usually accomplished by immersing the mold in water that has been de-aerated, as condensed gases in aerated water may form bubbles within the developed cavities of the mold. The container of water with the immersed mold is then placed in a chamber where a vacuum is used to facilitate the penetration of water into the mold features. A surfactant may be added to the water to lower its surface tension, further facilitating the wetting of the features. After the features are filled with water, the mold is then placed in the desired bath for electrodeposition, where the water in the features mixes with the bulk electrolyte. Depending on the feature geometry, some time is given for this mixing to occur before the electrodeposition of the mold is started. Planarization and Release – Electrodeposition is complete when all of the patterned features exhibit some degree of overplating. Due to wafer- and pattern-scale effects, the local deposition rate varies from point to point on the wafer, so the extent of overplating varies across the mold. This overplating must be removed mechanically, by grinding and/or lapping off the excess metal. Grinding is followed by a planarization step, yielding a mold with both the final desired thickness and an appropriate surface finish. After planarization, the PMMA is dissolved in a solvent, such as acetone, if the parts are to be freed from the wafer and used individually (direct LIGA). However, in some cases, a new, thick metal layer is deposited on top of the planarized surface to form a structural backing on top of the plated features in order to use the LIGA mold as an embossing tool for replication. Another way to accomplish the same end is by simply allowing the electrodeposited metal to grow completely out of the features, coalesce, and form into a monolithic metal disk. These latter two approaches are illustrated schematically in Fig. 4. After dissolution of the PMMA, if the plated features are going to be used as individual microparts themselves, the plating base layer must be dissolved to liberate the individual structures. Since copper is often used as a plating base and the LIGA structures themselves are often Ni or Ni alloys, chemical solutions selective to Cu may be used to dissolve the plating base, leaving the Ni unaffected. The microparts may then be collected and sorted for postprocessing metrology or testing required for the desired application.

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seed layer deposition

electrodeposition of LIGA features

electroplating

coalescence of LIGA features

resist dissolution & substrate removal

resist dissolution & substrate removal

Fig. 4 Process schemes for producing a thick tool bearing LIGA features for subsequent embossing or injection molding. (top) The LIGA mold is planarized so a new metal seed layer may be applied to the top of the mold, typically by vacuum deposition. A layer of thick Ni is then electroplated over the seed layer, after which the resist is dissolved and the substrate removed (either chemically or mechanically). (bottom) Electrodeposition is allowed to continue up and out of the resist until the overplated regions coalesce into a solid Ni piece. The substrate is removed as described in the prior approach. For this technique to work, it is necessary for the parts to be located close to one another so the overplated regions can join together

1.2 LIGA History Electrodeposition into features defined in resist by electron beam and X-ray lithography was first explored in the late 1960s and early 1970s by Romankiw and coworkers at IBM [21]. Also, the through-mask plating technology for producing gold X-ray masks necessary for X-ray exposures was developed by the same workers during this period. At the same time, through-mask electroplating was already becoming a preferred technique for the realization of patterned metal structures in the electronics industry for packaging and memory applications. It was thought possible that X-ray lithography would become necessary to replace optical lithography for features less than one micron. Romankiw gives a thorough review of the role of through-mask electroplating in the early stages of e-beam and X-ray lithography [21]. Figure 5 shows one of the earliest X-ray masks fabricated by Romankiw and co-workers by through-mask electroplating of gold using first an e-beam fabricated mask and subsequent X-ray lithography. The X-ray sources used up to 1973 by the group at IBM were laboratory sources and hence of low power. That year, highpower X-rays from a synchrotron in Hamburg, Germany, were employed by the IBM group to fabricate features in PMMA resist 12 ␮m thick and 1 ␮m wide. The separation between the features was 0.1 ␮m. Gold was electrodeposited to a thickness of 6 ␮m to fill the features, resulting in the first through-mask deposited structures in PMMA patterned with synchrotron radiation. These structures are shown in Fig. 6. Since such high aspect ratio features were not required for electronic devices, subsequent work by the group at IBM focused on thin structures having small lateral dimensions.

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Fig. 5 X-ray absorbing masks produced by Romankiw et al. by gold electrodeposition [21]. Photoresist patterns are on the left, while electroplated gold patterns are shown on the right. The top two images are from the original e-beam fabricated mask, resulting in an X-ray negative copy in the middle. The pattern was inverted another time to return to the original tone in the bottom two images. Reprinted from Electrochimica Acta, Vol. 43, L. T. Romankiw, A Path: From Electroplating Through Lithographic Masks in Electronics to LIGA in MEMS, pp. 2985–3005, Copyright (1997), with permission from Elsevier

By the early 1980s, investigations involving the fabrication of structures using features defined in thick PMMA resist by X-ray synchrotron radiation and subsequent electrodeposition were in progress at the Forschungzentrum Karlsruhe (FZK), in Karlsruhe, Germany. In this case, the researchers were not interested in the fabrication of electronic or magnetic devices, but instead in structures meant to be used for the isotopic separation of uranium [1]. Apparently, the critical features of the device needed to be not only very narrow but also very tall (i.e., high aspect ratio) for the separation process to work. X-ray lithography, with its capability to precisely form features having very small lateral dimensions in thick resist, was thus understandably an attractive fabrication technique for such structures. An example of one of the first devices fabricated at FZK is shown in Fig. 7. The potential of the technique relative to the fabrication of structures for microsystems became apparent,

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Fig. 6 Patterned PMMA 12 ␮m in thickness (left) exposed at the DESY accelerator in Hamburg and corresponding electroplated gold structures (right) as shown by Romankiw in ref. [21]. The resist-pattern line widths are 1 ␮m with 100-nm spacers, resulting in electroplated gold structures spaced 100 nm apart. Reprinted from Electrochimical Acta, Vol. 43, by L. T. Romankiw, “A Path: From Electroplating Through Lithographic Masks in Electronics to LIGA in MEMS”, pp. 2985–3005, Copyright (1997), with permission from Elsevier

Fig. 7 Patterned PMMA (left) and corresponding through-mold plated Ni nozzle structures for gas isotope separation (right) fabricated at the Forschungzentrum Karlsruhe [1]. The openings in the Ni of closest approach are about 3 ␮m. Reprinted from Naturwissenschaften, “Production of Separation-Nozzle Systems for Uranium Enrichment by a Combination of X-ray Lithography and Galvanoplastics”, by E. W. Becker, W. Ehrfeld, D. Muenchmeyer, H. Betz, A. Heuberger, S. Pongratz, W. Glashauser, H. J. Michel, and R. v. Siemens, Vol. 69, p. 520, Fig. 3, (1982, with permission of Springer-Verlag

and work continued on electroplating through PMMA resist to produce structures for other applications [3, 4, 22]. Furthermore, the researchers at FZK were interested in using X-ray lithography to form a metal master tool that would be subsequently used to mass-produce structures (presumably plastic) via embossing or injection-molding processes. Thus, the German acronym, LIGA, used generally to refer to electroplating through thick

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resist to form metal structures includes the word abformung, indicating the intention of using the metal structures as a tool to mass produce or replicate patterns. Subsequent to the establishment of the LIGA process at FZK in the early 1980s, X-ray lithography efforts elsewhere in the world began to appear, naturally centered at synchrotron facilities in Europe, Asia, and North America. Since then, a large body of LIGA research has been published in the literature and presented at international conferences. An attempt to comprehensively summarize the LIGA work that has been done over two decades would be beyond the scope of this chapter; thus, only a relatively small number of articles and presentations are referenced where appropriate to the topic at hand. It must be noted that many researchers worldwide (the current authors and their colleagues included) use X-ray lithography as a tool for fabricating a mold of structures, with the intention of using the electroplated parts separately in some sort of assembly (usually a microsystem). Although such a process does not involve the replication (abformung) step, practitioners still typically use the term LIGA to describe their work (occasionally this is referred to as “direct LIGA” as we have previously indicated). Since synchrotron radiation is usually necessary for the thick resist-exposure step, a large fraction of LIGA research groups are located in academic institutions or government-sponsored national laboratories. However, commercial companies have established their presence at such facilities, and some notable examples will be mentioned in the next section discussing applications of LIGA technology.

1.3 LIGA Applications In surveying the numerous articles and presentations involving the use of the LIGA technique, it is evident that an equally large number of applications for LIGAenabled structures have been proposed. However, over the course of the technology’s 20-year or so history, only a few of these proposed applications have been developed into commercial products. The need for an X-ray synchrotron source, no doubt an issue for those wishing to adapt the technology for larger-scale production, has been alleviated somewhat by the fact that most synchrotron facilities have active programs for allowing access by researchers and industry [14]. In this section, we discuss only the most popularly reported applications, with some emphasis on those that have been commercially realized to give the reader a general idea of the types of applications of interest. Good reviews are available for those interested in more detailed treatments of LIGA applications [2, 11, 13–15]. One of the most commonly discussed applications of structures fabricated via the LIGA process involves mechanical devices. Since lateral geometries in LIGA are defined lithographically, very high dimensional fidelity is theoretically possible across large areas, enabling the batch fabrication of large numbers of precision structures simultaneously. Moreover, deep, high-aspect-ratio structures are possible if thick resist is used, desirable for structures to be used as active devices

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transmitting useful amounts of mechanical energy.1 For example, the amount of torque that a micromotor can deliver is directly proportional to the height of the motor itself. Further, the use of electrodeposition as an additive materials-fabrication technique offers the possibility of a large materials set with interesting mechanical, magnetic, and electrical properties as compared to subtractive materials-fabrication techniques, such as silicon surface micromachining (some challenges in taking advantage of this potential materials set will be discussed in detail later). Gears, actuators, rotors, and drivers have been fabricated via the LIGA method for a large variety of purposes (see ref. [15] and references cited therein). Figures 1 and 8 show examples of LIGA structures fabricated from Ni-based electrodeposits at Sandia National Laboratories, Livermore (SNL), CA. Mechanical structures designed as sensors (motion, magnetic, pressure) have also been fabricated via the LIGA process. An SNL Ni accelerometer prototype device is shown in Fig. 9. Other LIGA researchers have fabricated similar structures (see, e.g., ref. [23] by Qu et al.). Christenson and Guckel have demonstrated several different types of mechanical devices, including linear and rotational actuators and micromotors [24]. An example of a minimotor assembly is shown in Fig. 10 [25]. This device was fabricated by the group at IBM using optical lithography and through-mask plating. More examples of such devices can be found in Madou [2]. Another area of application for LIGA-fabricated devices is in the field of optical systems and communications. The ability to produce thick structures that are highly parallel, with optical-quality side-wall roughness is useful in the fabrication of gratings, waveguides, and lenses [15]. These structures can be made from polymers that are directly patterned with X-rays, developed and used immediately

Fig. 8 Example of Ni test gear device formed from electrodeposition through a patterned PMMA mold. Micrograph courtesy of Georg Aigeldinger, Sandia National Laboratories, Livermore, California 1 This

is an important characteristic that distinguishes LIGA-fabricated microdevices from silicon MEMS technology.

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Fig. 9 Example of an acceleration-sensing prototype device fabricated by the LIGA process at Sandia National Laboratories, Livermore, California. The long, slender flexures are 25-␮m wide and 250-␮m tall; the entire width of the device is approximately 3 cm. A portion of the device is anchored in place, while another is free to move by the bending of the flexures, allowing for the sensing of acceleration. The device above is made of high-strength Ni

Permalloy core

Fig. 10 Minimotor assembly composed of piece parts formed by through-mask plating of thick and thin UV-photoresist by workers at IBM [25]. Electroplated copper and a nickel–iron alloy was necessary for its fabrication. The plated Cu coils are 60-␮m wide. Photograph reproduced with permission of the IBM Journal of Research and Development

Wire-bonding pad

Coil

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afterward. LIGA-fabricated structures have been developed for collimating grids for high-resolution solar-imaging missions [26] and adaptive optics systems in astronomy [27]. LIGA has enabled various connecting and mounting systems for optical fibers and components [2, 15]. The LIGA technique has been used to fabricate metal transmission lines with applications in the field of microwave- and millimeter-wave integrated circuits [28].

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The last area that can be broadly grouped as a LIGA application field is biological applications and microfluidics [15, 29] LIGA tools for embossing patterns into plastic structures to be used as platforms in disposable biological or medical applications (“biochips” or “lab-on-a-chip” devices) are of special interest, since such approaches are low in cost as compared to the direct LIGA route [30]. LIGA tools have also been employed for the microstructuring of composite materials used as artificial bone analogs to improve bone cell-growth conditions [31]. A range of microfluidic devices have been proposed, such as microreactors, micropumps, nozzles, and microvalves [32–34]. Both direct LIGA and the molding of plastic with a LIGA tool have been used for microfluidic device fabrication [35]. A few more applications that do not fit into the above categories are worth mentioning due to their unique use of LIGA technology. Spinnerets for synthetic microfiber production have been fabricated by LIGA to make high aspect ratio, narrow features of arbitrary prismatic cross-section [2, 13]. These are essentially nozzles for the extrusion of polymer material; the LIGA technique allows for finer features with smooth side walls as compared to conventional fabrication methods. The simultaneous batch production of large numbers of nozzle structures is more rapid than conventional machining, where one structure is formed at a time. Microscale cross-flow heat exchangers have been fabricated using a LIGA embossing tool and subsequent replication steps to form Ni metal microstructures with higher heat-transfer/volume ratios than conventional devices [36]. The possibility of using LIGA to form small Ni structures with microscale barbs for tagging has been explored and could be useful for military and law-enforcement applications [37]. In the area of defense, industry is studying the use of LIGA technology to fabricate fusing devices for munitions [38]. Some progress has been made in the last few years in the development of LIGAfabricated devices for commercial products. A number of optical, mechanical, and fluidic products are available from STEAG microParts, GmbH [39]. This company uses advanced injection-molding techniques in combination with LIGA technology to make inhalers, microspectrometers, and lab-on-a-chip reaction platforms, as well as other microfluidic products. Zero-backlash gears and other precision positioning systems are fabricated by Micromotion GmbH using a LIGA-related technique (see Fig. 11) [40]. LIGA technology has been employed to make optical fiber connectors by Spinner GmbH in collaboration with FZK [15]. In the United States, Axsun Technologies, Inc., uses the LIGA technique to make alignment structures for photonics systems [38]. As evidenced by this wide range of applications, the unique capability of the LIGA and LIGA-related techniques to fabricate high-aspect-ratio structures with a range of useful geometries has been known for several years. More recently, groups working on LIGA technology have started to focus on the fabrication of structures with special material properties. This often necessitates the consideration of materials other than electrodeposited Ni, in contrast to most of the examples discussed in this section. The next section discusses the unique challenges posed by the geometries encountered in the LIGA process during the electrodeposition of Ni and Ni alloys with special properties.

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Fig. 11 Precision position components fabricated by a LIGA-related process commercially available from Micromotion GmbH. Bottom image is a closeup of the gear assembly in the top photo. Photographs courtesy of Micromotion, GmbH

2 Electrodeposition into Deep High-Aspect-Ratio Features for LIGA 2.1 Introduction The science and process sensitivities of electrodeposition through thin resist2 used to produce metallic-conducting interconnects, packaging, and contacts for the microelectronics industry have been much discussed [16]. In contrast, electrodeposition through thick resist for deep, high aspect ratio LIGA features has received relatively little attention (although we note that one study involving design rules for the LIGA electrodeposition step has recently become available [41]). In surveying the literature where electrodeposition through patterned photoresist is discussed, it is evident that the microelectronics industry has devoted a significant amount of experimental and modeling resources to understanding through-mask electrodeposition (more

2 We

define “thin” resist loosely as less than several microns, while “thick” resist is considered to be hundreds of microns to several millimeters.

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detailed reviews of these developments are available) [16, 42]. A central theme of the prior literature is the classification of three length scales over which electrochemical processes occur; the first, the workpiece scale, involves the distribution of current over the scale of the substrate or wafer; the second, the pattern scale, involves the distribution of current between features defined in the insulating photoresist; the third, the feature scale, involves the distribution of current to and within an individual opening or feature in the resist. These three scales are depicted in Fig. 12 after DeBecker and West [43]. As will be discussed later, the principles governing the deposition of a metal structure or film having uniform thickness and properties over all these scales (usually desired for all electrodeposition processes) are largely the same, regardless of the final application. In terms of attaining uniformity across a substrate, the prior literature regarding the workpiece and pattern scales for electrodeposition through thin resist is directly applicable to electrodeposition through thick resist. The important difference regarding metal deposition through thin and thick resist comes when through-thickness uniformity is considered; as the electrodeposited metal films for microelectronics are usually only a few to several microns in thickness, appreciable through-thickness variations in film structure do not usually occur since the thickness is so small. Moreover, any small microstructural deviation that may be present through the film thickness does not usually critically impact the function of the electrodeposited metal film in microelectronics. But in contrast to the thin films employed in microelectronics, large variations in deposit microstructure may occur over the hundreds of microns that comprise the through-mask electrodeposited thick films in LIGA. Since most of the issues in attaining uniformity across the substrate are similar to those in microelectronics, this discussion focuses rather on attaining through-thickness uniformity in structures electrodeposited through thick resist, a challenging aspect unique to LIGA.

feature scale (cross sectional view)

Fig. 12 Schematic illustration of the workpiece, pattern, and feature scales, redrawn from a similar graphic from DeBecker and West [43]. Groups of features are distributed across the substrate; these groups consist of a patterned array of features. The feature scale involves a single feature and its internal uniformity

pattern scale

workpiece scale

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Besides differences in resist and metal thicknesses, another major difference between films electrodeposited for microelectronics and microsystem applications lies in the choice of materials. In microelectronics, the metal films are serving as conductors or contacts; hence, materials such as copper, gold, and lead–tin alloys (more recently, lead-free alternatives are under development) have attractive physical properties and are widely employed. In microsystems, the thick metal structures are typically serving as components in some mechanical device or as a replication mold; the mechanical properties are thus of most interest in these situations. Electrodeposited nickel has a long history of use as a structural material, since its mechanical properties may be tailored by the use of alloying elements and electrolyte bath additives (both organic and inorganic) [8, 44]. Depending on deposition conditions and chemistries, Ni may be electrodeposited with low stress, making thick films possible. The generally good corrosion resistance of electrodeposited Ni also makes it attractive for mechanical applications in a wide variety of environments. The material properties of Ni and Ni alloys will be discussed in more detail later in the chapter. In comparing electrodeposition processes for thin and thick resists, it is to be kept in mind that the materials that are deposited into these lithographic molds may have very different deposition characteristics as well.

2.2 Workpiece- and Pattern-Scale Effects In prior treatments of through-mask electrodeposition, the first length scale often identified is the workpiece scale; this is usually the characteristic length of the substrate (or wafer) itself onto which resist defining the desired structures has been applied. Variations in the local current density typically occur over the workpiece scale. The cell geometry, the size of the substrate, and other deposition parameters dictate the uniformity across the substrate; the degree of this uniformity may be described by the Wagner number, a dimensionless parameter that has been discussed in more detail previously [16]. Generally speaking, if no measures are taken to improve the current distribution across the wafer, regions close to the edge will have a locally higher current density than areas near the center of the substrate. A few different approaches may be used to render the current distribution across the wafer more uniform. The appropriate placement of insulating shields with respect to the wafer may result in a more uniform current distribution [45]. The use of auxiliary electrodes (also known as thief electrodes) in minimizing variations across the workpiece has been discussed previously [46]. For example, another cathode placed around the workpiece (as a type of surrounding “frame”) may improve the workpiece current distribution significantly. In industrial plating tools, all these aspects are carefully considered in optimizing the wafer-scale uniformity. Obviously, since a large number of wafers are typically run under fixed conditions in the microelectronics industry, a fair amount of time and effort is spent in finding the optimal cell geometry and deposition conditions. These approaches for homogenizing the wafer-scale uniformity are directly applicable to electrodeposition through thick resist in LIGA and have in some cases been adopted [45].

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The second length scale is referred to as the pattern scale. The relative amounts of exposed active metal and insulating photoresist may vary across the substrate due to the geometry and layout of the pattern defining the structures to be electrodeposited. Thus, the “active area density” varies depending on essentially the distribution of the insulating resist material. This leads to variations in the local current density (the deposition rate) depending on the local pattern geometry in the resist. Mehdizadeh et al. studied this problem for electrodeposition through photoresist having various pattern densities [47]. West et al. considered the effect of patterning on multiple electrodes of disks and lines [48]. These and other studies [16, 49] may be drawn upon in designing layouts where pattern-scale effects are minimized. In our experience, LIGA-pattern layouts that consist of an array of uniformly spaced features having similar dimensions are not commonly encountered; instead, patterns tend to consist of fine features (dense resist areas) located in close proximity to large, open areas of exposed seed metal (defining a wide, low aspect ratio feature). Thus, pattern-scale effects must be managed on a fairly routine basis. Although it may not be possible to alter the particular part geometry and size (necessary for the device function), some discretion may be exercised in distributing the features in the resist defining the part geometry so as to mitigate pattern-scale effects. Moreover, sacrificial features (openings in the resist) may be added to the pattern to break up areas that have long runs of uninterrupted insulating resist, resulting in a more uniform active area-density distribution [46–47]. This practice of inserting sacrificial “moats” or “frames” around features where dimensional fidelity is critical was previously mentioned with regard to minimizing dimensional errors due to PMMA swelling and thermal expansion after immersion in the electroplating bath [50]. It is somewhat fortuitous that the same measures that aid in minimizing these dimensional errors in LIGA also may help in rendering the pattern-scale current distribution more uniform. Mehdizadeh et al. have discussed the possibility of carefully considering the wafer- and pattern-scale current distribution and arranging features in the resist across the workpiece so as to attain a more balanced current distribution [47]. Even when detailed current distribution models are unavailable, past experience can be a useful guide in judiciously arranging the part layout to avoid uneven distributions of current at the pattern scale.

2.3 The Feature Scale As mentioned previously, the similarity between microelectronics processing and LIGA through-mask electrodeposition diminishes as one moves from the workpiece and pattern to the feature scale. The principal reason for this is the large resist thicknesses typically employed for X-ray lithography. As pointed out by Dukovic [16], at the feature scale, the dimensions of the lithographic features are usually small enough (microns) that electrical-field effects become less important, and the influence of the concentration field of the reacting species grows in determining the feature scale current distribution. Since mixing is limited inside the feature due to the

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presence of the surrounding resist material, the concentration of a reacting species may vary with position within the feature. Another aspect that must be considered for both thin and thick resists is that as deposition proceeds, the feature geometry changes as the deposited metal fills the feature. Generally speaking, obtaining good mixing inside lithographic features becomes more difficult with increasing resist thickness. When the electrodepostion reaction involves just a single metal cation, variations in its concentration inside the feature typically result in variations in the local rate of deposition and therefore deposit thickness [51]. The deposition characteristics of copper, gold, and tin alloys through relatively thin resists (less than 20 microns) for bump structures have been considered with attention to the thickness distribution of the deposit within a single feature [52–57]. It is desirable that these bump structures have good as-plated uniformity for subsequent packaging processing. Another example of an important feature-scale electrodeposition problem is the case of copper Damascene electrodeposition for copper interconnects [58]; for this process, proprietary electrolyte bath additives and active feature side walls lead to more complicated feature-filling behavior, despite the fact that only a single elemental species is being deposited [59, 60] The understanding and control of through-mask electrodeposition at the feature scale has undoubtedly been important in enabling the use of these processes for the large-scale manufacturing of microelectronics packaging and copper interconnects [16, 42] In the case of electrodeposition through thick resist for LIGA, the importance of the feature scale is not its influence on the local deposit-thickness uniformity (the wafer is planarized after plating, removing thickness variations across the wafer at all scales). Rather, it is the more serious issue of poor mixing in the mold features themselves due to their small widths and large heights. This has broad implications with respect to the potential for variations in the concentrations of electrolyte species that may, in turn, impact the local deposit composition, morphology, and properties. For example, if additives or other metal species are present as alloying elements, profound changes may occur through the thickness owing to the constantly changing feature geometry that accompanies the metal growth. If the concentration of one of these species is close to zero at the feature bottom (due to its rapid incorporation into the deposit, for example), large changes in the flux of this species will occur as the deposit grows, and the diffusion length from the bulk electrolyte shortens. The resulting nonuniform deposit morphology or alloy composition may be unacceptable for some applications. The electrodeposition of the NiCo and NiMn systems and the resulting feature-scale uniformity will be contrasted to demonstrate the importance of transport into LIGA features later in the chapter. Interesting experiments involving the feature scale were carried out by Leyendecker et al. [61]. These authors studied the effect of thick photoresist on mass transport and on the pH within a LIGA feature using special electrodes. In the first series of experiments, a rotating disk electrode masked by an insulating patterned polymer layer of various thicknesses and feature sizes is employed to study a model redox reaction occurring under transport control. The aqueous electrolyte consists of 2 mM potassium ferro- and ferri-cyanide each in 1 M potassium chloride at 25◦ C.

98 rpm 1.6 limiting current density (mA/cm2)

Fig. 13 Limiting current densities for ferri–ferro cyanide redox couple on bare and patterned rotating-disk electrodes replotted from the results of Leyendecker et al. [61]. Feature hole diameter is 200 ␮m. The presence of the resist has a large effect on the transport of species to the feature bottom, even for an aspect ratio of one. Solid points are the bare rotating disk electrode, while the hollow points are electrodes patterned with resists of various thicknesses as indicated

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Results of their experiments are reproduced in Fig. 13; although various geometries were investigated, they present results for a constant hole diameter of 200 ␮m and resist heights of 100, 200, and 500 ␮m (in addition to an unmasked electrode). In the case of an unpatterned, bare rotating disk, good linearity is obtained as expected by plotting the limiting current density as a function of the square root of the electrode rotation rate 1/⍀0.5. When the electrode is covered with photoresist, the difficulty in generating mixing into the features becomes evident. For a hole diameter of 200 ␮m and a resist height of 100 ␮m (an aspect ratio of 0.5) the measured limiting current densities are close to those on the bare electrode. But for a resist thickness of 200 ␮m (aspect ratio 1), the measured limiting current densities are much lower than for unpatterned electrodes and the electrode with 100 ␮m of resist. Even at this modest aspect ratio, increasing the electrode-rotation rate becomes less effective at transporting reactant to the electrode surface, resulting in a flatter curve for the 200-␮m thick resist in Fig. 13. When the resist thickness becomes 500 ␮m (aspect ratio 2.5), almost no increase is obtained in the limiting current density with increasing rotation rate. This is somewhat surprising, since if metal deposition through thick resist occurred under transport control, one would expect impractically low deposition rates to be necessary for the deep, high-aspectratio features used in LIGA process. In fact, structures with aspect ratios of 10 having appreciable thicknesses (hundreds of microns) are not uncommon, and, while on the low end of the current-density operating range, these structures are typically deposited at rates that are not drastically lower than those conventionally used in electroplating and electroforming. The reasons for this seeming discrepancy will become apparent when other modes of transport are discussed.

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In the same paper [61], Leyendecker et al. perform a second series of experiments investigating the pH behavior within a deep, high aspect ratio feature as Ni is electroplated into the feature. As the current efficiency during Ni electrodeposition is not always 100%, the pH may rise close to the cathode surface (especially in a feature in thick resist), resulting in the presence of adsorbed hydroxide species that may affect the deposit morphology. Since Ni is often electrodeposited for LIGA applications, these experiments are highly relevant. Special PMMA structures were fabricated by laminating three 10-␮m thick antimony metal foils in between 240-␮m thick PMMA layers; the laminated structure was then bonded to a metal substrate. Microholes were drilled through the layers until the conducting substrate was reached. The final structure thus consists of a metal plating base with four levels of PMMA separated by the antimony sheets, through which arrays of microholes are drilled, the entire piece is approximately 1000 ␮m in thickness. Figure 14 is a schematic diagram of the laminated structure taken after Leyendecker et al. [61]. The antimony metal acts as a pH sensor due to the pH-dependent equilibrium with its oxide. The Sb/Sb2 O3 system has been used previously as a pH probe. By monitoring the potential between the antimony sheets and a reference antimony electrode in the bulk electrolyte, the authors could study in situ the pH in the LIGA feature as Ni electrodeposition occurred. This is the only study of its kind in the literature of which the current authors are aware. Results of filling these features were given in this paper for the 200 ␮m diameter microholes. They are reproduced in Fig. 15. Nickel is deposited into the features at 50 mA/cm2 from a sulfamate bath (76 g/L Ni and 40 g/L boric acid) at 52◦ C and a bulk pH of 3.8. Since the exact depth of the drilled features was not known (the drilling proceeded some distance into the bulk metal piece used as the plating base), deposition occurs until the first Sb layer is overgrown. At that point, plating is stopped (the position of the Ni deposit surface within the features is then known) and the experiment paused until the pH in the feature returns to the bulk pH. Then, plating resumes, with the potential of the second Sb layer monitored until the growing Ni deposit reaches this Sb layer. Ni deposition continues from that point with

drilled microholes Sb sheets

PMMA

contact wires for pH

Conducting cathode substrate

Fig. 14 Diagram of special microstructured pH electrode used by Leyendecker et al. [61], redrawn after a similar sketch that was reported [61]. Feature hole diameters of 200, 100, and 50 ␮m were considered. The Sb sheets embedded in the PMMA resist function as in situ pH electrodes, allowing for the monitoring of local pH within the features as electrodeposition proceeds from the cathode at the bottom of the features

100

pH at 2nd Sb layer

Ni growth direction

5.5

pH at a Sb electrode

Fig. 15 In situ pH measurements from the microstructured pH electrode shown in the previous figure, replotted from Leyndecker et al. [61]. In this case, the hole diameter of all features is 200 ␮m. The inset helps one visualize the position of the Sb pH electrode layers with respect to the growing Ni deposit. A Ni sulfamate bath was used operating at 50◦ C and a current density of 50 mA/cm2

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the potential of the third Sb layer then being monitored until it too is overgrown by the Ni deposit. Thus, the zero value on the x ordinate in Fig. 15 represents the point when the Ni is even with the first Sb layer (about 750 ␮m from the feature mouth into the bulk electrolyte). The plotted values represent the pH measured at the respective Sb layers (fixed in position) as the Ni fills the features in the laminated structure. The pH at the second Sb layer (500 ␮m from the feature mouth) is as high as 5.5 when the Ni deposition begins. As it grows, the second Sb layer pH value drops toward 4.5. After the Ni deposit grows past the second Sb layer, the third Sb layer (itself 250 ␮m from the feature mouth) is monitored. The measured pH values at the third Sb layer are just slightly higher than the bulk value of 3.8. Finally, when the Ni deposit has grown to a point just below the depth of the third Sb layer, the pH at that position is close to that in the bulk. These results are important for a number of reasons. First of all, although the PMMA feature thickness corresponding to the zero position on the x axis is 750 ␮m, the aspect ratio of this feature is only 3.75, which is not considered to be very aggressive for LIGA electrodeposition (aspect ratios of 10–15 approach the high end of what is commonly fabricated). Despite this modest aspect ratio, the measured pH 500 ␮m from the feature mouth is as high as 5.5; if the pH near the growing Ni surface is this high or higher (a likely case, since protons are consumed at the interface) the deposit morphology could be profoundly influenced. Deposition at high pH values has been typically associated with high hardnesses and the possible incorporation of oxygen into the deposit, presumably from hydroxide species adsorbed at the deposit surface [8, 44, 62–63]. As the deposit grows, the microstructure of the deposit may therefore change as the feature opening is approached, and the pH drops toward its value in the bulk electrolyte. If the pH value reaches extremely high values, the impurities in the deposit from hydroxide species may compromise

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its material properties. Another issue is that the increasing pH is indicative of hydrogen generation within the feature; if the hydrogen trapped within the feature accumulates and forms a bubble, it may be occluded into the deposit as a defect that can lead to failure. These issues are of real concern for structures that will be used in mechanical applications, especially for structures having aspect ratios more extreme than those considered in Fig. 15. Another series of experiments relevant to the feature scale in LIGA involving transport limitations is reported by Griffiths et al. [64]. They use a commercial Ni sulfamate plating electrolyte to deposit Ni into features drilled into PMMA. A single piece of Cu foil attached to one side of the PMMA acts as the substrate, from which the deposited Ni structures could be removed for weighing in the determination of the current efficiency. Current densities range from 1.1 to 108 mA/cm2 , and an electrolyte temperature of 38◦ C is employed. The drilled microholes have diameters of 1.7, 3.2, and 6.4 mm and depths from 17 to 42 mm. They also calculate the Sherwood number (the ratio between the measured current to the diffusion-limited current) for each case. The experimental results are surprising in that the Sherwood numbers are all between 10 and 100, indicating a much larger deposition current than expected based upon the diffusion-limited case. The reported data for the experimental conditions are reproduced in Table 1 [64]. Measured current efficiencies indicate that hydrogen evolution accounts for only a few percent of the total current (except in one case, where the current efficiency was only 89%), suggesting that the large current densities are associated with the metal deposition reaction itself. They also indicate their results were reproducible, further suggesting that the observed behavior was not due to hydrogen evolution. The authors explain the unexpectedly high currents as resulting from enhanced transport of the reacting metal ion due to natural convection in the feature driven by its depletion at the substrate. This hypothesis is further supported by the fact that when the experimental cell was inverted, the measured currents were an order of magnitude less than with the deposition surface facing up.

Table 1 Experimental data reproduced from Griffiths et al. [62]. Experimentally measured currents during through-mask electrodeposition into microfeatures drilled into PMMA show current densities larger than those expected from pure diffusion as indicated by the Sherwood number. The authors explain that buoyancy-driven convection is an important mode of transport in LIGA features Cavity diameter (mm)

Feature aspect ratio

Current density (mA/cm2 )

Current efficiency

Sherwood number

1.7 1.7 1.7 3.18 6.35

10 15 25 8 1.6

11 86 86 86 108

99.7 96.4 89.6 99.5 100.9

48.0 82.2 137.5 82.2 41.1

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These authors go on to demonstrate by numerical modeling that flow across the top of the features cannot support the transport of the reacting metal ions at the observed rates, and that instead buoyancy-driven flows are probably important in allowing such high deposition rates [64]. Nilson and Griffiths present more detailed calculations of natural convection in high aspect ratio trenches in a subsequent article [65]. They find that the relative importance of natural convection depends on the feature geometry and the inclination of the substrate. The authors conclude that some mixing from natural convection is expected to occur in features having aspect ratios less than 1.2, 6.6, and 37 for resist thicknesses of 0.1, 1.0, and 10 mm, respectively. Thus, natural convection becomes important for a wider range of feature aspect ratios as the resist thickness increases. Since resist thicknesses in microelectronics are usually only tens of microns or less, the importance of convective flow had not been widely discussed until electrodeposition into deep LIGA features was considered. It is interesting to contrast the findings of Leyendecker et al. [61], discussed at the beginning of this section, with those of Griffiths et al. [64]. In the former case, the insulating PMMA mask was shown to have strongly diminished mixing, resulting in lower transport rates of the reacting ions, while in the latter case, buoyancy-driven transport rates into deep highaspect-ratio features higher than those expected from pure diffusion control were observed. Since Leyendecker et al. used a redox couple to measure transport rates through microstructured electrodes, they were not able to benefit from potential buoyancy-driven flows induced by the consumption of metal ions at the feature bottom. Another series of studies focusing on feature-scale uniformity in LIGA was carried out by Schwartz and co-workers [66–68]. Leith et al. considered the electrodeposition of NiFe at 23◦ C from sulfamate-chloride chemistries having various ratios of Ni to Fe electrolyte loadings [67]. They pointed out that the plating characteristics of an electrolyte must be carefully considered before employing it for through-mask electrodeposition using thick resist. They found that electrolytes having less dissolved iron (e.g., 20:1 Ni2+ :Fe2+ as opposed to 10:1 and 5:1 also considered in their study) are less sensitive to mixing variations at relatively high current densities, suggesting that they would be more suitable for the electrodeposition of LIGA structures. Leith and Schwartz also describe a cell designed to maximize workpiece- and pattern-scale uniformity, using the NiFe system (since it is a challenging system for uniformity) to demonstrate good uniformity across the wafer [67]. The throughthickness uniformity was not investigated in this study [67]. In another article, Wang et al. used an electrolyte with a 10:1 Ni2+ :Fe2+ loading (where the deposited NiFe alloy composition is more sensitive to mixing) to study convective-diffusion conditions during the through-mask deposition of LIGA structures [68]. They term the approach “process archaeology” since the plated structure was planarized to half its deposited thickness for compositional analysis via energy dispersive X-ray analysis [68]. By observing in plan view the planarized structures, regions in the feature where locally high degrees of mixing occur could be easily identified since the Fe content of the alloy increases with mixing. In this case, the authors were using the

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transport-sensitive deposition kinetics of the Fe as a type of “tracer” tool to study the mixing within small cavities such as LIGA resist features. Another group of authors also considered the NiFe system to focus on the featurescale uniformity of through-mask-deposited LIGA structures. Thommes et al. used a sulfate-based NiFe electrolyte at 50◦ C with a Ni2+ :Fe2+ ratio of about 12:1 to deposit NiFe structures at 5 mA/cm2 with good through-thickness uniformity [69]. Figure 16, reproduced from their data, shows the compositional behavior of the deposition system using a rotating-disk electrode. It is clear from Fig. 16 that for low current densities, the electrode-rotation rate does not influence the deposited alloy composition, suggesting that under these conditions the alloy composition is not greatly influenced by the amount of mixing. This relative insensitivity to mixing would appear promising for the feature-scale uniformity of LIGA NiFe structures. The suitability of the authors’ deposition conditions for the electrodeposition of uniform high aspect ratio NiFe microstructures is evidenced by the throughthickness compositional data shown in Fig. 17. For a resist thickness of 180 ␮m and a feature line width of 8 ␮m (aspect ratio 22.5), the authors obtained very good NiFe alloy uniformity throughout the entire structure thickness using a deposition current density of 5 mA/cm2 . Through-thickness uniformity suffers at higher deposition current densities. Figure 17 also shows experimental results for deposition at 14 mA/cm2 using the same feature geometry. The Fe content increases through the deposit as the top PMMA surface is approached, varying from about 20% to 50% across the thickness. Though not shown here, the authors filled cylindrical features with a diameter of 5 ␮m and a height of 90 ␮m depositing NiFe at 5 mA/cm2 . They

50

40

% Fe

30

Fig. 16 Electrodeposited NiFe alloy composition dependence on deposition conditions, for conditions given by and replotted from Thommes et al. [69]. The relative compositional insensitivity at low current densities suggests that the system may be appropriate for the electrodeposition of uniform, high-aspect-ratio structures

20 200 rpm 10

500 rpm 1000 rpm 20

40

60

80

(current density mA/cm2)

100

104 100 open 5 mA/cm2

solid 14 mA/cm2

80 % composition

Fig. 17 Electrodeposited NiFe alloy composition through-thickness uniformity replotted from Thommes et al. [69]. The structure width is 8 ␮m and its height is 180 ␮m. Open points are for deposition at 5 mA/cm2 , while the solid points are at 14 mA/cm2 . Deposition at the lower current density (where composition was shown to be less sensitive to mixing) leads to uniform alloy content through the structure thickness, as compared to 14 mA/cm2

J.J. Kelly and S.H. Goods

60 Fe Ni 40

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0

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height (μm)

show similarly good results as for the structure in Fig. 17 deposited at the same current density. The electrodeposition process outlined by Thommes et al. has been shown to be capable of producing high-aspect-ratio structures with good alloy throughthickness compositional uniformity [69]. To the authors’ knowledge, few other studies exist of alloy deposition through thick resist where the feature-scale uniformity is considered in such detail. An aspect that is likely important in explaining the good results obtained by these authors is the bath temperature; Brenner has discussed the fact that NiFe electrodeposition becomes less anomalous (and hence less transport sensitive) with increasing bath temperature [70]. Andricacos and Romankiw also discuss the importance of bath temperature as well as other process variables on electrodeposited magnetic alloy composition [71]. Given the limitations in obtaining good mixing in small LIGA features, it is not surprising that achieving good feature-scale uniformity for anomalous deposition systems (such as NiFe) is challenging for geometries encountered in LIGA electrodeposition [70–71]. New techniques are being employed for studying the electrodeposition reaction inside of small features like those fabricated by the LIGA process; for example, special microelectrodes and chronoamperometric methods have been developed to measure the local metal cation concentrations during alloy electrodeposition inside small cavities [72]. Kuepper and Schultze study concentration variations inside of a cavity where a NiCu alloy is being electrodeposited [72]; they also observe the formation of a Ni hydroxide and nickel oxide at the deposition surface during electrodeposition of the NiCu alloy from a sulfate electrolyte with potassium nitrate as supporting electrolyte. It is likely that specialized, in situ techniques such as those used by Kuepper and Schultze [72] and others [61] will yield new insights into electrodeposition into deep high-aspect-ratio features.

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3 Summary: Uniformity at the Workpiece, Pattern, and Feature Scales in LIGA The detailed study of Thommes et al. is a good example of the considerable effort required to develop an electrodeposition process capable of producing uniform structures at the feature scale for geometries encountered in LIGA electrodeposition. When mixing effects are important (as often the case in Ni-alloy deposition) [70–71], this is especially difficult. After some confidence in the feature-scale uniformity is attained for a given chemistry and set of deposition conditions, the uniformity at the pattern and workpiece scales must still be addressed as well. This makes LIGA through-mask electrodeposition in some ways more challenging than electrodeposition through thin resist, as the feature scale adds literally another dimension to the problem of obtaining uniformity across multiple length scales. Considerable time and effort may be saved by first characterizing the electrodeposition kinetics and the importance of mass transport for an electrodeposition process before attempting to apply it to LIGA fabrication (especially in the case of an alloy system). If one has a good understanding of kinetics, transport, and alloy composition, electrolytes and deposition parameters suitable for deposition through thick resist may be chosen more prudently [67, 69]. Examples of such situations will be given when the mechanical properties of electrodeposits are discussed.

4 Electrodeposition in LIGA: Materials and Other Aspects Up to this point, the range and types of materials electrodeposited for LIGA applications have not been discussed in depth. In the next section, we will go into more detail on these topics in regard to requirements for LIGA-fabricated structures to be used in mechanical applications. Before doing so, we briefly mention materials studied for other types of LIGA applications, as well as other aspects related to the integration of the electrodeposition step into the LIGA process. Besides the study of Thommes et al. discussed above as an example of featurescale uniformity [69], the possibility of using electrodeposited NiFe structures as magnetic components in microsystems has been discussed or demonstrated in a number of articles (a sampling is given in the references) [25, 73–79]; but as shown by Thommes et al. [69], some care must be taken in insuring that a given deposition process will result in acceptable alloy uniformity. Chin reviews a variety of different types of magnet films, besides the traditional plated iron-group alloys for applications in microsystems, discussing the potential of electrodeposition in fabricating some more exotic magnetic alloys [80]. Despite the challenges posed by the thick resist often used in LIGA, the possibility of electroplating magnetic alloys for LIGA microstructures with useful magnetic properties makes LIGA and LIGA-like processes attractive to microsystem designers. In general, such LIGA-fabricated NiFe microstructures appear to have magnetic properties that are comparable to similar bulk NiFe materials [75–76, 78].

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Compared with Ni and Ni alloys, investigations of other electroplated materials for LIGA processing are relatively few in number; this is most likely due to the fact that Ni may be electroplated with low stress in thick films with reasonable mechanical properties, as discussed in the next section. However, copper [28] and gold [21] (both of which can be plated as thick films) have been used with the LIGA process to fabricate thick-plated LIGA structures. Copper is of interest of course where a high electrical conductivity is necessary, and gold is attractive when structures having a high mass are required due to its high density (˜19.3 g/cm3 ). One study reports the electrodeposition of a Bi–Te alloy into a LIGA mold to form BiTe microposts for microcooling probes [81]. Though not discussed at length here, another important area of LIGA electrodeposition research involves the nucleation and adhesion of the plated structures to the seed layer material used as the substrate. Since the substrate is exposed to X-rays during the exposure of the PMMA resist, metallization layers between the substrate and resist (such as those commonly used as plating bases, like copper) can reemit the X-ray radiation (e.g., by fluorescence), damaging the bond at the resist-metallization interface and provoking adhesion failures during subsequent processing [82]. Since this damage can lead to the failure of the entire LIGA mold, alternative plating bases that do not behave in such a way are thus of interest [82]. At the Forschungzentrum Karlsruhe in Germany, an approach using TiO2 as a plating base has been developed and successfully employed [83]. Other suitable plating base materials have been recommended, but electrodeposition processes where good nucleation and adhesion to the base still need to be developed for these materials [82]. In this section, the challenges in attaining good uniformity in deposit morphology and/or deposit alloy composition over various length scales during the LIGA electrodeposition process step was emphasized. In practice, an equally important aspect in electrodeposition for LIGA is the subject of electrolyte ageing and maintenance. Although it is not the focus of this chapter, a few comments on these topics are appropriate, especially since they are little discussed in the LIGA electrodeposition literature. These aspects are particularly important if the LIGA process is to be used for the manufacturing of a product with some specified, reproducible material properties that depend on the deposit morphology and/or alloy composition. For example, sulfamate baths are very popular for the electrodeposition of Ni LIGA microstructures. But as the electrolyte is used and ages, ammonium ions (originating from the sulfamate ion) may accumulate and adsorb at the deposition surface, acting as an additive and changing the deposit morphology and hardness [84]. Moreover, it has been known from the traditional electroforming literature that sulfurcontaining breakdown species (originating presumably from the sulfamate ion) may also accumulate over time, leading to changes in film stress and morphology [85]. Both of these aging effects complicate the deposition of a film, with consistent morphology and stress during manufacturing. We have observed complications arising from sulfamate electrolyte aging during the deposition of a NiMn alloy from this chemistry [86]. Since the aging of electrolytes often leads to species that induce unwanted changes in the plated film microstructure and material properties that an electrodeposition process is engineered to obtain, an understanding of electrolyte

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ageing and maintenance is critical for the use of LIGA as a manufacturing process. Before addressing these topics in more detail, we first discuss the development of electrodeposited materials for LIGA mechanical applications in the next section.

5 Properties and Structure of Electrodeposited Materials for LIGA-Based Microsystem Applications 5.1 Introduction We describe here the material characteristics necessary to successfully fabricate precision structures for microsystem applications. In particular, we focus on the electrodeposited (ED) component structures that are required to have mechanical functionality: for example, springs or flexures. In such instances, mechanical strength, ductility, fatigue life, and a well-characterized modulus are critical material properties that must be well understood and reproducible. These structures typically have micron-scale tolerances with respect to critical dimensions and insofar as their mechanical and physical behavior are governed by their submicron grain size, crystallographic texture, and the very high defect densities typical of electrodeposits, we may consider these materials to be nanostructured. In this section we restrict ourselves largely to the material properties and performance of structures that are fabricated via the LIGA process, which we described at the beginning of this chapter. In some instances, though, we refer to work based on the deposition of blanket films where LIGA-prototyping processes were not employed. A number of constraints limit the range of practical electrolytes and therefore electrodeposited material systems. Some of these constraints include: (1) low bath temperatures, which often must be well below those recommended by common electrodeposition practice (necessary to reduce thermal distortions of the resist material that define the lateral dimensions of precision structures) [50, 87]; (2) transport limitations – particularly important in deep, high-aspect-ratio features where circulation of the bulk electrolyte is impeded, being typically minimized by the use of reduced deposition rates (i.e., the use of atypically low current densities) [86]; (3) low intrinsic film stresses to minimize piece-part distortions and survivability of the mold during plating; and (4) pH compatibility with LIGA-fabricated molds and substrates and pH control (both in the bulk electrolyte as well as within narrow, stagnant cavities as described in the previous section). These various factors are summarized in Table 2. With regard to the properties of electrodeposits themselves, where structures have an intended mechanical functionality, the most critical material property considerations are (1) strength – as section size of microscale components decrease, the strength must increase to avoid plastic deformation; (2) ductility – structures within mechanical assemblies cannot fail in a brittle, catastrophic fashion; (3) modulus – the material stiffness is a first order input parameter in the design of a spring or flexure; and (4) fatigue – the fatigue response of an electrodeposit can be an important

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J.J. Kelly and S.H. Goods Table 2 Deposition-process characteristics and requirements

Characteristic

Requirement

Near-ambient temperature deposition Transport: Cation/impurity/additive

Dimensional tolerances Composition, microstructure, property uniformity in high aspect ratio features Contour tolerances Thick-section deposit Substrate/resist compatibility, effects on ED structure and properties

Intrinsic film stress pH restrictions

Table 3 Electrodeposit properties and requirements Characteristic

Requirement

Strength Ductility Well-characterized modulus Fatigue

Elastic response of mechanically functional structures Preclude catastrophic brittle fracture Predictable flexural response Predictable response to dynamic environments

material property depending on the ambient or functional environment. Table 3 summarizes these requirements. The practical choice of ED materials compatible with all aspects of LIGA fabrication is restricted to gold, copper, and nickel (and a limited number of nickelbased alloys). Not withstanding this limited family of materials, the range of microstructures and resulting material properties is quite extensive, and it is the electrochemistry of metal deposition that is principally responsible for defining the microstructure and properties of these materials which form the free-standing structures from which microsystem component parts are fabricated. However, with respect to the fabrication of mechanically functional structures, neither gold nor copper has suitable strength (yield strength of ED copper is typically less than 500 MPa, while even “hard” gold will rarely exhibit yield strengths that exceed 250–300 MPa) [8]. We focus then on ED nickel and Ni-based alloys since these materials can exhibit yield strengths that range between 350 MPa and 1200 MPa, depending on electrolyte and the particular plating conditions employed. The main challenge lies in adapting approaches that have been used for years to deposit high-strength Ni for industrial electroforming and electroplating to the through-mask electrodeposition of LIGA structures.

5.2 Measurement Techniques for Strength and Ductility The strength of electrodeposits can be characterized either indirectly through surface indentation hardness t